R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1  (2005-06-20), ISBN 3-900051-07-0

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> ### * <HEADER>
> ###
> attach(NULL, name = "CheckExEnv")
> assign(".CheckExEnv", as.environment(2), pos = length(search())) # base
> ## add some hooks to label plot pages for base and grid graphics
> setHook("plot.new", ".newplot.hook")
> setHook("persp", ".newplot.hook")
> setHook("grid.newpage", ".gridplot.hook")
> 
> assign("cleanEx",
+        function(env = .GlobalEnv) {
+ 	   rm(list = ls(envir = env, all.names = TRUE), envir = env)
+            RNGkind("default", "default")
+ 	   set.seed(1)
+    	   options(warn = 1)
+ 	   delayedAssign("T", stop("T used instead of TRUE"),
+ 		  assign.env = .CheckExEnv)
+ 	   delayedAssign("F", stop("F used instead of FALSE"),
+ 		  assign.env = .CheckExEnv)
+ 	   sch <- search()
+ 	   newitems <- sch[! sch %in% .oldSearch]
+ 	   for(item in rev(newitems))
+                eval(substitute(detach(item), list(item=item)))
+ 	   missitems <- .oldSearch[! .oldSearch %in% sch]
+ 	   if(length(missitems))
+ 	       warning("items ", paste(missitems, collapse=", "),
+ 		       " have been removed from the search path")
+        },
+        env = .CheckExEnv)
> assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now
> assign("ptime", proc.time(), env = .CheckExEnv)
> grDevices::postscript("wle-Examples.ps")
> assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv)
> options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly"))
> options(warn = 1)    
> library('wle')
> 
> assign(".oldSearch", search(), env = .CheckExEnv)
> assign(".oldNS", loadedNamespaces(), env = .CheckExEnv)
> cleanEx(); ..nameEx <- "binary"
> 
> ### * binary
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: binary
> ### Title: Convert decimal base number to binary base
> ### Aliases: binary
> ### Keywords: arith
> 
> ### ** Examples
> 
> binary(2)
$binary
[1] 0 1

$dicotomy
[1] FALSE  TRUE

> binary(10,dim=5)
$binary
[1] 0 1 0 1 0

$dicotomy
[1] FALSE  TRUE FALSE  TRUE FALSE

> 
> 
> 
> cleanEx(); ..nameEx <- "mle.aic"
> 
> ### * mle.aic
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: mle.aic
> ### Title: Akaike Information Criterion
> ### Aliases: mle.aic
> ### Keywords: regression
> 
> ### ** Examples
> 
> library(wle)
> 
> data(hald)
> 
> cor(hald)
           [,1]       [,2]       [,3]        [,4]        [,5]
[1,]  1.0000000  0.7307175  0.8162526 -0.53467068 -0.82130504
[2,]  0.7307175  1.0000000  0.2285795 -0.82413376 -0.24544511
[3,]  0.8162526  0.2285795  1.0000000 -0.13924238 -0.97295500
[4,] -0.5346707 -0.8241338 -0.1392424  1.00000000  0.02953700
[5,] -0.8213050 -0.2454451 -0.9729550  0.02953700  1.00000000
> 
> result <- mle.aic(y.hald~x.hald)
> 
> summary(result,num.max=10)

Call:
mle.aic(formula = y.hald ~ x.hald)


Akaike Information Criterion (AIC):
      (Intercept) x.hald1 x.hald2 x.hald3 x.hald4   aic
 [1,]           1       1       1       0       0 62.83
 [2,]           1       1       1       0       1 63.17
 [3,]           1       1       1       1       0 63.19
 [4,]           1       1       0       1       1 63.65
 [5,]           0       1       1       1       1 63.94
 [6,]           1       1       1       1       1 65.15
 [7,]           1       1       0       0       1 65.64
 [8,]           1       0       1       1       1 67.49
 [9,]           1       0       0       1       1 82.52
[10,]           0       1       1       0       1 84.03

Printed the first  10  best models 
> 
> 
> 
> cleanEx(); ..nameEx <- "mle.cp"
> 
> ### * mle.cp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: mle.cp
> ### Title: Mallows Cp
> ### Aliases: mle.cp
> ### Keywords: regression
> 
> ### ** Examples
> 
> library(wle)
> 
> data(hald)
> 
> cor(hald)
           [,1]       [,2]       [,3]        [,4]        [,5]
[1,]  1.0000000  0.7307175  0.8162526 -0.53467068 -0.82130504
[2,]  0.7307175  1.0000000  0.2285795 -0.82413376 -0.24544511
[3,]  0.8162526  0.2285795  1.0000000 -0.13924238 -0.97295500
[4,] -0.5346707 -0.8241338 -0.1392424  1.00000000  0.02953700
[5,] -0.8213050 -0.2454451 -0.9729550  0.02953700  1.00000000
> 
> result <- mle.cp(y.hald~x.hald)
> 
> summary(result)

Call:
mle.cp(formula = y.hald ~ x.hald)


Mallows Cp:
     (Intercept) x.hald1 x.hald2 x.hald3 x.hald4    cp
[1,]           1       1       1       0       0 2.678
[2,]           1       1       1       0       1 3.018
[3,]           1       1       1       1       0 3.041
[4,]           1       1       0       1       1 3.497
[5,]           0       1       1       1       1 3.793
[6,]           1       1       1       1       1 5.000

Printed the first  6  best models 
> 
> plot(result)
> 
> 
> 
> cleanEx(); ..nameEx <- "mle.cv"
> 
> ### * mle.cv
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: mle.cv
> ### Title: Cross Validation Selection Method
> ### Aliases: mle.cv
> ### Keywords: regression
> 
> ### ** Examples
> 
> library(wle)
> 
> data(hald)
> 
> cor(hald)
           [,1]       [,2]       [,3]        [,4]        [,5]
[1,]  1.0000000  0.7307175  0.8162526 -0.53467068 -0.82130504
[2,]  0.7307175  1.0000000  0.2285795 -0.82413376 -0.24544511
[3,]  0.8162526  0.2285795  1.0000000 -0.13924238 -0.97295500
[4,] -0.5346707 -0.8241338 -0.1392424  1.00000000  0.02953700
[5,] -0.8213050 -0.2454451 -0.9729550  0.02953700  1.00000000
> 
> result <- mle.cv(y.hald~x.hald)
> 
> summary(result)

Call:
mle.cv(formula = y.hald ~ x.hald)


Cross Validation selection criteria:
      (Intercept) x.hald1 x.hald2 x.hald3 x.hald4      cv
 [1,]           1       1       1       0       0   9.851
 [2,]           1       1       1       0       1  12.260
 [3,]           1       1       0       0       1  12.450
 [4,]           1       1       1       1       0  12.900
 [5,]           1       1       0       1       1  13.660
 [6,]           0       1       1       1       1  14.810
 [7,]           1       0       1       1       1  18.020
 [8,]           1       1       1       1       1  24.430
 [9,]           1       0       0       1       1  30.090
[10,]           0       1       1       0       1  35.540
[11,]           1       0       1       1       0  70.170
[12,]           1       0       0       0       1 108.000
[13,]           1       0       1       0       0 109.600
[14,]           0       0       1       0       1 132.100
[15,]           0       0       1       1       1 145.000
[16,]           1       0       1       0       1 154.900
[17,]           1       1       0       0       0 156.400
[18,]           0       1       1       1       0 166.600
[19,]           1       0       0       1       0 235.800
[20,]           1       1       0       1       0 245.200

Printed the first  20  best models 
> 
> 
> 
> cleanEx(); ..nameEx <- "mle.stepwise"
> 
> ### * mle.stepwise
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: mle.stepwise
> ### Title: Stepwise, Backward and Forward selection methods
> ### Aliases: mle.stepwise
> ### Keywords: regression
> 
> ### ** Examples
> 
> 
> library(wle)
> 
> data(hald)
> 
> cor(hald)
           [,1]       [,2]       [,3]        [,4]        [,5]
[1,]  1.0000000  0.7307175  0.8162526 -0.53467068 -0.82130504
[2,]  0.7307175  1.0000000  0.2285795 -0.82413376 -0.24544511
[3,]  0.8162526  0.2285795  1.0000000 -0.13924238 -0.97295500
[4,] -0.5346707 -0.8241338 -0.1392424  1.00000000  0.02953700
[5,] -0.8213050 -0.2454451 -0.9729550  0.02953700  1.00000000
> 
> result <- mle.stepwise(y.hald~x.hald)
> 
> summary(result)

Call:
mle.stepwise(formula = y.hald ~ x.hald)


 Forward  selection procedure

F.in:  4 

Last  3  iterations:
     (Intercept) x.hald1 x.hald2 x.hald3 x.hald4        
[1,]           1       0       0       0       1  22.800
[2,]           1       1       0       0       1 108.200
[3,]           1       1       1       0       1   5.026

> 
> 
> 
> 
> cleanEx(); ..nameEx <- "plot.mle.cp"
> 
> ### * plot.mle.cp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: plot.mle.cp
> ### Title: Plot the Mallows Cp
> ### Aliases: plot.mle.cp
> ### Keywords: regression
> 
> ### ** Examples
> 
> library(wle)
> 
> data(hald)
> 
> result <- mle.cp(y.hald~x.hald)
> 
> plot(result,num.max=7)
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "plot.wle.cp"
> 
> ### * plot.wle.cp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: plot.wle.cp
> ### Title: Plot the Weighted Mallows Cp
> ### Aliases: plot.wle.cp
> ### Keywords: regression robust
> 
> ### ** Examples
> 
> library(wle)
> x.data <- c(runif(60,20,80),runif(5,73,78))
> e.data <- rnorm(65,0,0.6)
> y.data <- 8*log(x.data+1)+e.data
> y.data[61:65] <- y.data[61:65]-4
> z.data <- c(rep(0,60),rep(1,5))
> plot(x.data, y.data, xlab="X", ylab="Y")
> xx.data <- cbind(x.data, x.data^2, x.data^3, log(x.data+1))
> result <- wle.cp(y.data~xx.data)
> plot(result,num.max=15)
> 
> 
> 
> cleanEx(); ..nameEx <- "plot.wle.lm"
> 
> ### * plot.wle.lm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: plot.wle.lm
> ### Title: Plots for the Linear Model
> ### Aliases: plot.wle.lm
> ### Keywords: regression robust
> 
> ### ** Examples
> 
> library(wle)
> 
> data(artificial)
> 
> result <- wle.lm(y~x1+x2+x3, data=artificial, boot=40, group=6, num.sol=2)
> 
> result

Call:
wle.lm(formula = y ~ x1 + x2 + x3, data = artificial, boot = 40,     group = 6, num.sol = 2)

Coefficients:
      (Intercept)  x1        x2        x3      
[1,]  -0.19670      0.08969   0.03875  -0.05298
[2,]  -0.94351      0.15653   0.18912   0.18152

Scale estimate:  0.5561 0.6688

Number of solutions  2 

> 
> plot.wle.lm(result) # all plots, default behavior 
> 
> plot.wle.lm(result, roots=1) # only first root, one plot for window 
> 
> par(mfcol=c(2,2))
> plot.wle.lm(result, roots=1) # only first root, as usual
> 
> plot.wle.lm(result, roots=2, which=1, which.main=0)
> # only second root, only residual vs fitted values plot
> 
> plot.wle.lm(result, which=1)
> # main plot + residual vs fitted values plot for each root
> 
> par(mfcol=c(3,2))
> plot.wle.lm(result, which=1)
> # main plot + residual vs fitted values plot for each root all in the same window
> 
> 
> 
> 
> graphics::par(get("par.postscript", env = .CheckExEnv))
> cleanEx(); ..nameEx <- "wle.aic"
> 
> ### * wle.aic
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.aic
> ### Title: Weighted Akaike Information Criterion
> ### Aliases: wle.aic
> ### Keywords: regression robust
> 
> ### ** Examples
> 
> library(wle)
> 
> x.data <- c(runif(60,20,80),runif(5,73,78))
> e.data <- rnorm(65,0,0.6)
> y.data <- 8*log(x.data+1)+e.data
> y.data[61:65] <- y.data[61:65]-4
> z.data <- c(rep(0,60),rep(1,5))
> 
> plot(x.data,y.data,xlab="X",ylab="Y")
> 
> xx.data <- cbind(x.data,x.data^2,x.data^3,log(x.data+1))
> colnames(xx.data) <- c("X","X^2","X^3","log(X+1)")
> 
> result <- wle.aic(y.data~xx.data,boot=10,group=10,num.sol=2)
> 
> summary(result)

Call:
wle.aic(formula = y.data ~ xx.data, boot = 10, group = 10, num.sol = 2)


Weighted Akaike Information Criterion (WAIC):
      (Intercept) xx.dataX xx.dataX^2 xx.dataX^3 xx.datalog(X+1)   waic
 [1,]           1        0          0          0               1  92.27
 [2,]           0        1          0          0               1  92.66
 [3,]           0        0          1          0               1  93.38
 [4,]           0        0          1          1               1  93.62
 [5,]           0        1          0          1               1  93.91
 [6,]           0        1          1          0               1  94.06
 [7,]           1        0          0          1               1  94.25
 [8,]           1        0          1          0               1  94.27
 [9,]           1        1          0          0               1  94.27
[10,]           0        0          0          1               1  94.31
[11,]           1        1          1          1               1  94.57
[12,]           1        1          1          0               0  94.89
[13,]           0        1          1          1               1  95.14
[14,]           1        0          1          1               1  95.39
[15,]           1        1          0          1               1  95.65
[16,]           1        1          1          0               1  95.85
[17,]           1        1          0          1               0  96.30
[18,]           1        1          1          1               0  96.61
[19,]           0        0          0          0               1  97.46
[20,]           1        0          1          1               0 107.70

Printed the first  20  best models 
> 
> result <- wle.aic(y.data~xx.data+z.data,boot=10,group=10,num.sol=2)
> 
> summary(result)

Call:
wle.aic(formula = y.data ~ xx.data + z.data, boot = 10, group = 10, 
    num.sol = 2)


Weighted Akaike Information Criterion (WAIC):
      (Intercept) xx.dataX xx.dataX^2 xx.dataX^3 xx.datalog(X+1) z.data  waic
 [1,]           1        0          0          0               1      1 101.0
 [2,]           0        1          0          0               1      1 101.4
 [3,]           0        0          1          0               1      1 102.2
 [4,]           0        0          1          1               1      1 102.2
 [5,]           0        1          0          1               1      1 102.5
 [6,]           0        1          1          0               1      1 102.7
 [7,]           1        1          1          1               1      1 102.9
 [8,]           1        0          0          1               1      1 102.9
 [9,]           1        0          1          0               1      1 103.0
[10,]           1        1          0          0               1      1 103.0
[11,]           0        0          0          1               1      1 103.1
[12,]           1        1          1          0               0      1 103.4
[13,]           0        1          1          1               1      1 103.6
[14,]           1        0          1          1               1      1 103.9
[15,]           1        1          0          1               1      1 104.2
[16,]           1        1          1          0               1      1 104.5
[17,]           1        1          0          1               0      1 104.7
[18,]           1        1          1          1               0      1 105.2
[19,]           0        0          0          0               1      1 106.1
[20,]           1        0          1          1               0      1 116.0

Printed the first  20  best models 
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "wle.aic.ar"
> 
> ### * wle.aic.ar
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.aic.ar
> ### Title: Weighted Akaike Information Criterion for AR models
> ### Aliases: wle.aic.ar wle.ar.wls
> ### Keywords: robust ts
> 
> ### ** Examples
> 
> 
> data(rocky)
> 
> res <- wle.aic.ar(x=rocky, order=c(6,0), group=50, group.start=30, method="WLS")
> res

Call:
wle.aic.ar(x = rocky, order = c(6, 0), group = 50, group.start = 30, 
    method = "WLS")


Weighted Akaike Information Criterion (WAIC):
      ar sar include.mean  waic
 [1,]  0   0            1 530.8
 [2,]  6   0            1 537.7
 [3,]  3   0            0 859.3
 [4,]  5   0            0 859.9
 [5,]  4   0            0 861.1
 [6,]  3   0            1 861.3
 [7,]  6   0            0 861.9
 [8,]  5   0            1 861.9
 [9,]  2   0            0 862.5
[10,]  4   0            1 863.1
[11,]  2   0            1 864.5
[12,]  1   0            0 873.3
[13,]  1   0            1 875.3

Printed the first  13  best models 
> plot(res$full.model$weights)
> 
> 
> 
> cleanEx(); ..nameEx <- "wle.ar"
> 
> ### * wle.ar
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.ar
> ### Title: Fit Autoregressive Models to Time Series - Preliminary Version
> ### Aliases: wle.ar wle.ar.ao wle.ar.start wle.ar.step wle.ar.matrix
> ### Keywords: robust ts
> 
> ### ** Examples
> 
> data(lh)
> wle.ar(x=lh, order=c(3,0), group=30) 
$coef
        ar1         ar2         ar3   intercept 
 0.57515582 -0.07746981 -0.19993021  1.63941419 

$sigma2.coef
       ar1        ar2        ar3  intercept 
0.01666993 0.02203779 0.01322118 0.07534020 

$sigma2
[1] 0.1851104

$arma
    ar     ma    sar    sma period   diff  sdiff 
     3      0      0      0      1      0      0 

$resid
Time Series:
Start = 1 
End = 48 
Frequency = 1 
          1           2           3           4           5           6 
 0.76058581 -0.61978816 -0.43386060 -0.15402810 -0.13899693 -0.69697532 
          7           8           9          10          11          12 
 0.40038515 -0.12621441  0.01580331 -0.43928368 -0.23621181 -0.37744509 
         13          14          15          16          17          18 
 0.12987398 -0.59319091  1.03562028  0.29937932 -0.17213503 -0.10465482 
         19          20          21          22          23          24 
 0.14418818 -0.29451183 -0.22193019 -0.34517114  0.55236538  0.32697816 
         25          26          27          28          29          30 
-0.49583877 -0.19005157 -0.01175463  0.72505328  0.14743398  0.01715682 
         31          32          33          34          35          36 
 0.31212517 -0.10336879  0.38670749 -0.01682718 -0.55852716 -0.26894857 
         37          38          39          40          41          42 
-0.49790091 -0.61057486  0.11145374  0.86111164  0.40516051  0.52304427 
         43          44          45          46          47          48 
 0.37845449  0.14850286 -0.09490716  1.37396376  0.08756118  0.21836916 

$resid.without.ao
Time Series:
Start = 1 
End = 48 
Frequency = 1 
 [1]  0.76058581 -0.61978816 -0.43386060 -0.15402810 -0.13899693 -0.69697532
 [7]  0.40038515 -0.12621441  0.01580331 -0.43928368 -0.23621181 -0.37744509
[13]  0.12987398 -0.59319091  1.03562028  0.29937932 -0.17213503 -0.10465482
[19]  0.14418818 -0.29451183 -0.22193019 -0.34517114  0.55236538  0.32697816
[25] -0.49583877 -0.19005157 -0.01175463  0.72505328  0.14743398  0.01715682
[31]  0.31212517 -0.10336879  0.38670749 -0.01682718 -0.55852716 -0.26894857
[37] -0.49790091 -0.61057486  0.11145374  0.86111164  0.40516051  0.52304427
[43]  0.37845449  0.14850286 -0.09490716  1.37396376  0.08756118  0.21836916

$resid.with.ao
Time Series:
Start = 1 
End = 48 
Frequency = 1 
 [1]  0.76058581 -0.61978816 -0.43386060 -0.15402810 -0.13899693 -0.69697532
 [7]  0.40038515 -0.12621441  0.01580331 -0.43928368 -0.23621181 -0.37744509
[13]  0.12987398 -0.59319091  1.03562028  0.29937932 -0.17213503 -0.10465482
[19]  0.14418818 -0.29451183 -0.22193019 -0.34517114  0.55236538  0.32697816
[25] -0.49583877 -0.19005157 -0.01175463  0.72505328  0.14743398  0.01715682
[31]  0.31212517 -0.10336879  0.38670749 -0.01682718 -0.55852716 -0.26894857
[37] -0.49790091 -0.61057486  0.11145374  0.86111164  0.40516051  0.52304427
[43]  0.37845449  0.14850286 -0.09490716  1.37396376  0.08756118  0.21836916

$x.ao
Time Series:
Start = 1 
End = 48 
Frequency = 1 
 [1] 2.4 2.4 2.4 2.2 2.1 1.5 2.3 2.3 2.5 2.0 1.9 1.7 2.2 1.8 3.2 3.2 2.7 2.2 2.2
[20] 1.9 1.9 1.8 2.7 3.0 2.3 2.0 2.0 2.9 2.9 2.7 2.7 2.3 2.6 2.4 1.8 1.7 1.5 1.4
[39] 2.1 3.3 3.5 3.5 3.1 2.6 2.1 3.4 3.0 2.9

$call
wle.ar(x = lh, order = c(3, 0), group = 30)

$series
[1] "lh"

$weights
        1         2         3         4         5         6         7         8 
0.8770214 0.8513499 0.9842693 0.9685031 0.9562108 0.9763833 0.9122962 0.9478814 
        9        10        11        12        13        14        15        16 
0.9980096 0.9816906 0.9987265 0.9901146 0.9473250 0.8583436 0.6223688 0.9959195 
       17        18        19        20        21        22        23        24 
0.9837913 0.9585056 0.9463381 0.9894398 0.9983096 0.9832950 0.9884632 0.9889650 
       25        26        27        28        29        30        31        32 
0.9618264 0.9953712 0.9970886 0.9083033 0.9516891 0.9988067 0.9825639 0.9608227 
       33        34        35        36        37        38        39        40 
0.9129801 0.9997837 0.9804700 0.9996453 0.9617339 0.8332837 0.9843228 0.8415040 
       41        42        43        44        45        46        47        48 
0.9241724 0.9952801 0.9353634 0.9538838 0.9800901 0.2406930 0.9784559 0.7477231 

$weights.with.ao
 [1] 0.8770201 0.8513511 0.9842691 0.9685028 0.9562109 0.9763832 0.9122955
 [8] 0.9478819 0.9980095 0.9816905 0.9987265 0.9901147 0.9473258 0.8583447
[15] 0.6223692 0.9959196 0.9837911 0.9585063 0.9463386 0.9894398 0.9983096
[22] 0.9832950 0.9884627 0.9889649 0.9618263 0.9953713 0.9970886 0.9083015
[29] 0.9516894 0.9988068 0.9825638 0.9608232 0.9129796 0.9997837 0.9804706
[36] 0.9996453 0.9617339 0.8332842 0.9843234 0.8415045 0.9241718 0.9952797
[43] 0.9353622 0.9538848 0.9800905 0.2406931 0.9784566 0.7477230

$weights.without.ao
 [1] 0.8770201 0.8513511 0.9842691 0.9685028 0.9562109 0.9763832 0.9122955
 [8] 0.9478819 0.9980095 0.9816905 0.9987265 0.9901147 0.9473258 0.8583447
[15] 0.6223692 0.9959196 0.9837911 0.9585063 0.9463386 0.9894398 0.9983096
[22] 0.9832950 0.9884627 0.9889649 0.9618263 0.9953713 0.9970886 0.9083015
[29] 0.9516894 0.9988068 0.9825638 0.9608232 0.9129796 0.9997837 0.9804706
[36] 0.9996453 0.9617339 0.8332842 0.9843234 0.8415045 0.9241718 0.9952797
[43] 0.9353622 0.9538848 0.9800905 0.2406931 0.9784566 0.7477230

$tot.sol
[1] 1

$not.conv
[1] 0

$ao.position
$ao.position[[1]]
NULL


attr(,"class")
[1] "wle.arima"
> 
> 
> 
> cleanEx(); ..nameEx <- "wle.binomial"
> 
> ### * wle.binomial
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.binomial
> ### Title: Robust Estimation in the Binomial Model
> ### Aliases: wle.binomial print.wle.binomial
> ### Keywords: models robust
> 
> ### ** Examples
> 
> library(wle)
> 
> set.seed(1234)
> 
> x <- rbinom(20,p=0.2,size=10)
> wle.binomial(x,size=10)

Call:
wle.binomial(x = x, size = 10)

p:
      [,1]  
[1,]  0.1791


Number of solutions  1 

> 
> x <- c(rbinom(20,p=0.2,size=10),rbinom(10,p=0.9,size=10))
> wle.binomial(x,size=10)

Call:
wle.binomial(x = x, size = 10)

p:
      [,1]  
[1,]  0.2053


Number of solutions  1 

> 
> 
> 
> 
> cleanEx(); ..nameEx <- "wle.cp"
> 
> ### * wle.cp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.cp
> ### Title: Weighted Mallows Cp
> ### Aliases: wle.cp
> ### Keywords: regression robust
> 
> ### ** Examples
> 
> library(wle)
> 
> x.data <- c(runif(60,20,80),runif(5,73,78))
> e.data <- rnorm(65,0,0.6)
> y.data <- 8*log(x.data+1)+e.data
> y.data[61:65] <- y.data[61:65]-4
> z.data <- c(rep(0,60),rep(1,5))
> 
> plot(x.data,y.data,xlab="X",ylab="Y")
> 
> xx.data <- cbind(x.data,x.data^2,x.data^3,log(x.data+1))
> colnames(xx.data) <- c("X","X^2","X^3","log(X+1)")
> 
> result <- wle.cp(y.data~xx.data,boot=10,group=10,num.sol=2)
> 
> summary(result)

Call:
wle.cp(formula = y.data ~ xx.data, boot = 10, group = 10, num.sol = 2)


Weighted Mallows Cp:
    (Intercept)        xx.dataX      xx.dataX^2      xx.dataX^3 xx.datalog(X+1) 
              1               1               1               1               1 
            wcp 
              5 

Printed the first  1  best models 
> 
> plot(result,num.max=15)
> 
> result <- wle.cp(y.data~xx.data+z.data,boot=10,group=10,num.sol=2)
> 
> summary(result)

Call:
wle.cp(formula = y.data ~ xx.data + z.data, boot = 10, group = 10, 
    num.sol = 2)


Weighted Mallows Cp:
    (Intercept)        xx.dataX      xx.dataX^2      xx.dataX^3 xx.datalog(X+1) 
              1               1               1               1               1 
         z.data             wcp 
              1               6 

Printed the first  1  best models 
> 
> plot(result,num.max=15)
> 
> 
> 
> cleanEx(); ..nameEx <- "wle.cv"
> 
> ### * wle.cv
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.cv
> ### Title: Model Selection by Weighted Cross-Validation
> ### Aliases: wle.cv
> ### Keywords: regression robust
> 
> ### ** Examples
> 
> library(wle)
> 
> set.seed(1234)
> 
> x.data <- c(runif(60,20,80),runif(5,73,78))
> e.data <- rnorm(65,0,0.6)
> y.data <- 8*log(x.data+1)+e.data
> y.data[61:65] <- y.data[61:65]-4
> z.data <- c(rep(0,60),rep(1,5))
> 
> plot(x.data,y.data,xlab="X",ylab="Y")
> 
> xx.data <- cbind(x.data,x.data^2,x.data^3,log(x.data+1))
> colnames(xx.data) <- c("X","X^2","X^3","log(X+1)")
> 
> result <- wle.cv(y.data~xx.data,boot=20,num.sol=2)
> 
> summary(result)

Call:
wle.cv(formula = y.data ~ xx.data, boot = 20, num.sol = 2)


Weighted Cross Validation selection criteria:
      (Intercept) xx.dataX xx.dataX^2 xx.dataX^3 xx.datalog(X+1)    wcv
 [1,]           0        0          0          1               1 0.3409
 [2,]           0        0          1          0               1 0.3411
 [3,]           0        1          0          0               1 0.3426
 [4,]           1        0          0          0               1 0.3477
 [5,]           0        0          0          0               1 0.3519
 [6,]           1        0          1          0               1 0.3873
 [7,]           0        1          1          0               1 0.3880
 [8,]           1        0          0          1               1 0.3887
 [9,]           1        1          0          0               1 0.3887
[10,]           0        1          0          1               1 0.3923
[11,]           0        0          1          1               1 0.3981
[12,]           1        1          1          0               0 0.4294
[13,]           1        1          1          1               0 0.4537
[14,]           0        1          1          1               1 0.4595
[15,]           1        1          0          1               0 0.4623
[16,]           1        0          1          1               1 0.4672
[17,]           1        1          0          1               1 0.4730
[18,]           1        1          1          0               1 0.4795
[19,]           1        1          0          0               0 0.5453
[20,]           1        0          1          1               0 0.6071

Printed the first  20  best models 
> 
> result <- wle.cv(y.data~xx.data+z.data,boot=20,num.sol=2,
+               monte.carlo=1000,split=50)
> 
> summary(result)

Call:
wle.cv(formula = y.data ~ xx.data + z.data, monte.carlo = 1000, 
    split = 50, boot = 20, num.sol = 2)


Weighted Cross Validation selection criteria:
      (Intercept) xx.dataX xx.dataX^2 xx.dataX^3 xx.datalog(X+1) z.data    wcv
 [1,]           0        1          0          0               1      1 0.3987
 [2,]           0        0          1          0               1      1 0.3988
 [3,]           0        0          0          1               1      1 0.3999
 [4,]           1        0          0          0               1      1 0.4011
 [5,]           0        0          0          0               1      1 0.4125
 [6,]           0        1          1          0               1      1 0.4169
 [7,]           0        1          0          1               1      1 0.4175
 [8,]           1        0          0          1               1      1 0.4176
 [9,]           1        0          1          0               1      1 0.4180
[10,]           0        0          1          1               1      1 0.4187
[11,]           1        1          0          0               1      1 0.4192
[12,]           1        1          1          0               0      1 0.4415
[13,]           1        1          1          0               1      1 0.4462
[14,]           1        1          0          1               1      1 0.4476
[15,]           1        1          1          1               0      1 0.4485
[16,]           1        0          1          1               1      1 0.4489
[17,]           0        1          1          1               1      1 0.4501
[18,]           1        1          0          1               0      1 0.4610
[19,]           1        1          1          1               1      1 0.5028
[20,]           1        0          1          1               0      1 0.5556

Printed the first  20  best models 
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "wle.gamma"
> 
> ### * wle.gamma
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.gamma
> ### Title: Robust Estimation in the Gamma model
> ### Aliases: wle.gamma print.wle.gamma
> ### Keywords: models robust
> 
> ### ** Examples
> 
> library(wle)
> 
> x <- rgamma(n=100, shape=2, scale=2)
> 
> wle.gamma(x)

Call:
wle.gamma(x = x)

Scale:
[1]  1.499

Rate:
[1]  0.667

Shape:
[1]  2.479


Number of solutions  1 

> 
> x <- c(rgamma(n=30, shape=2, scale=2), rgamma(n=100, shape=20, scale=20))
> 
> wle.gamma(x, boot=10, group=10, num.sol=2) # depending on the sample, one or two roots.  

Call:
wle.gamma(x = x, boot = 10, group = 10, num.sol = 2)

Scale:
[1]  495.6

Rate:
[1]  0.002018

Shape:
[1]  0.5887


Number of solutions  1 

> 
> 
> 
> 
> cleanEx(); ..nameEx <- "wle.lm"
> 
> ### * wle.lm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.lm
> ### Title: Fitting Linear Models using Weighted Likelihood
> ### Aliases: wle.lm
> ### Keywords: robust regression
> 
> ### ** Examples
> 
> library(wle)
> # You can find this data set in:
> # Hawkins, D.M., Bradu, D., and Kass, G.V. (1984). 
> # Location of several outliers in multiple regression data using
> # elemental sets. Technometrics, 26, 197-208.
> #
> data(artificial)
> 
> result <- wle.lm(y.artificial~x.artificial,boot=40,num.sol=3)
> 
> summary(result)

Call:
wle.lm(formula = y.artificial ~ x.artificial, boot = 40, num.sol = 3)

Root  1

Weighted Residuals:
    Min      1Q  Median      3Q     Max 
-1.2517 -0.4987  0.0000  0.5422  1.3085 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)   -0.94351    0.12792  -7.376 3.46e-10 ***
x.artificial1  0.15653    0.07809   2.005 0.049112 *  
x.artificial2  0.18912    0.07168   2.638 0.010382 *  
x.artificial3  0.18152    0.05021   3.615 0.000581 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.6688 on 66.03095 degrees of freedom
Multiple R-Squared: 0.9665,	Adjusted R-squared: 0.965 
F-statistic: 634.7 on 3 and 66.03095 degrees of freedom,	p-value:     0 


Call:
wle.lm(formula = y.artificial ~ x.artificial, boot = 40, num.sol = 3)

Root  2

Weighted Residuals:
    Min      1Q  Median      3Q     Max 
-0.9095 -0.3758  0.0000  0.3889  1.0291 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)  
(Intercept)   -0.19670    0.10419  -1.888    0.064 .
x.artificial1  0.08969    0.06655   1.348    0.183  
x.artificial2  0.03875    0.04076   0.951    0.346  
x.artificial3 -0.05298    0.03549  -1.493    0.141  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.5561 on 58.6243 degrees of freedom
Multiple R-Squared: 0.04914,	Adjusted R-squared: 0.0004795 
F-statistic:  1.01 on 3 and 58.6243 degrees of freedom,	p-value: 0.3949 

> 
> plot(result)
> 
> 
> 
> cleanEx(); ..nameEx <- "wle.lm.summaries"
> 
> ### * wle.lm.summaries
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.lm.summaries
> ### Title: Accessing Linear Model Fits for wle.lm
> ### Aliases: coef.wle.lm formula.wle.lm fitted.wle.lm model.frame.wle.lm
> ###   summary.wle.lm summary.wle.lm.root weights.wle.lm print.wle.lm
> ###   print.summary.wle.lm print.summary.wle.lm.root
> ### Keywords: robust regression
> 
> ### ** Examples
> 
> library(wle)
> # You can find this data set in:
> # Hawkins, D.M., Bradu, D., and Kass, G.V. (1984). 
> # Location of several outliers in multiple regression data using
> # elemental sets. Technometrics, 26, 197-208.
> #
> data(artificial)
> 
> result <- wle.lm(y.artificial~x.artificial,boot=40,group=6,num.sol=3)
> 
> #summary only for the first root
> summary(result,root=1)

Call:
wle.lm(formula = y.artificial ~ x.artificial, boot = 40, group = 6, 
    num.sol = 3)

Root  1

Weighted Residuals:
    Min      1Q  Median      3Q     Max 
-1.2517 -0.4987  0.0000  0.5422  1.3085 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)   -0.94351    0.12792  -7.376 3.46e-10 ***
x.artificial1  0.15653    0.07809   2.005 0.049112 *  
x.artificial2  0.18912    0.07168   2.638 0.010382 *  
x.artificial3  0.18152    0.05021   3.615 0.000581 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.6688 on 66.03095 degrees of freedom
Multiple R-Squared: 0.9665,	Adjusted R-squared: 0.965 
F-statistic: 634.7 on 3 and 66.03095 degrees of freedom,	p-value:     0 

> #summary for all the roots
> summary(result,root="ALL")

Call:
wle.lm(formula = y.artificial ~ x.artificial, boot = 40, group = 6, 
    num.sol = 3)

Root  1

Weighted Residuals:
    Min      1Q  Median      3Q     Max 
-1.2517 -0.4987  0.0000  0.5422  1.3085 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)   -0.94351    0.12792  -7.376 3.46e-10 ***
x.artificial1  0.15653    0.07809   2.005 0.049112 *  
x.artificial2  0.18912    0.07168   2.638 0.010382 *  
x.artificial3  0.18152    0.05021   3.615 0.000581 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.6688 on 66.03095 degrees of freedom
Multiple R-Squared: 0.9665,	Adjusted R-squared: 0.965 
F-statistic: 634.7 on 3 and 66.03095 degrees of freedom,	p-value:     0 


Call:
wle.lm(formula = y.artificial ~ x.artificial, boot = 40, group = 6, 
    num.sol = 3)

Root  2

Weighted Residuals:
    Min      1Q  Median      3Q     Max 
-0.9095 -0.3758  0.0000  0.3889  1.0291 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)  
(Intercept)   -0.19670    0.10419  -1.888    0.064 .
x.artificial1  0.08969    0.06655   1.348    0.183  
x.artificial2  0.03875    0.04076   0.951    0.346  
x.artificial3 -0.05298    0.03549  -1.493    0.141  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.5561 on 58.62431 degrees of freedom
Multiple R-Squared: 0.04914,	Adjusted R-squared: 0.0004795 
F-statistic:  1.01 on 3 and 58.62431 degrees of freedom,	p-value: 0.3949 

> 
> 
> 
> cleanEx(); ..nameEx <- "wle.normal"
> 
> ### * wle.normal
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.normal
> ### Title: Robust Estimation in the Normal Model
> ### Aliases: wle.normal
> ### Keywords: models robust
> 
> ### ** Examples
> 
> library(wle)
> 
> data(cavendish)
> 
> result <- wle.normal(cavendish)
> 
> result

Call:
wle.normal(x = cavendish)

Location:
[1]  5.469

Scale:
[1]  0.1879


Number of solutions  1 

> 
> result <- wle.normal(cavendish,boot=20,num.sol=1)
> 
> barplot(result$weights,col=2,xlab="Observations",
+         ylab="Weights",ylim=c(0,1),
+         names.arg=seq(1:length(result$weights)))
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "wle.normal.mixture"
> 
> ### * wle.normal.mixture
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.normal.mixture
> ### Title: Robust Estimation in the Normal Mixture Model
> ### Aliases: wle.normal.mixture wle.normal.mixture.start
> ###   print.wle.normal.mixture
> ### Keywords: robust models
> 
> ### ** Examples
> 
> library(wle)
> set.seed(1234)
> x <- c(rnorm(150,0,1),rnorm(50,15,2))
> wle.normal.mixture(x,m=2,group=50,group.start=2,boot=5,num.sol=3)

Call:
wle.normal.mixture(x = x, m = 2, boot = 5, group = 50, num.sol = 3,     group.start = 2)

Location:
      [,1]     [,2]   
[1,]  15.1904  -0.1167
[2,]  15.1924  -0.1167

Scale:
      [,1]    [,2]  
[1,]  1.9546  0.9294
[2,]  1.9356  0.9298

Proportion:
      [,1]    [,2]  
[1,]  0.2370  0.7630
[2,]  0.2215  0.7785


Number of solutions  2 

> wle.normal(x,group=2,boot=10,num.sol=3)

Call:
wle.normal(x = x, boot = 10, group = 2, num.sol = 3)

Location:
[1]  -0.1171   4.1823

Scale:
[1]  0.9375  7.0449


Number of solutions  2 

> 
> 
> 
> 
> cleanEx(); ..nameEx <- "wle.normal.multi"
> 
> ### * wle.normal.multi
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.normal.multi
> ### Title: Robust Estimation in the Normal Multivariate Model
> ### Aliases: wle.normal.multi
> ### Keywords: models multivariate robust
> 
> ### ** Examples
> 
> library(wle)
> 
> data(iris)
> 
> smooth <- wle.smooth(dimension=4,costant=4,
+                     weight=0.5,interval=c(0.3,0.7))
> 
> x.data <- as.matrix(iris[iris[,5]=="virginica",1:4])
> 
> result <- wle.normal.multi(x.data,boot=20,group=21,
+                            num.sol=3,smooth=smooth$root)
> 
> result

Call:
wle.normal.multi(x = x.data, boot = 20, group = 21, num.sol = 3,     smooth = smooth$root)

Location:
Sepal.Length   Sepal.Width  Petal.Length   Petal.Width  
       6.535         2.964         5.495         2.020  


Variance-Covariance matrix:
[[1]]
              Sepal.Length  Sepal.Width  Petal.Length  Petal.Width
Sepal.Length       0.31930      0.07328       0.22985      0.03729
Sepal.Width        0.07328      0.08363       0.05881      0.04542
Petal.Length       0.22985      0.05881       0.23008      0.03834
Petal.Width        0.03729      0.04542       0.03834      0.07090



Number of solutions  1 

> 
> result <- wle.normal.multi(x.data,boot=20,group=21,
+                            num.sol=1,smooth=smooth$root)
> 
> barplot(result$weights,col=2,xlab="Observations",
+        ylab="Weights",ylim=c(0,1),
+        names.arg=seq(1:length(result$weights)))
> 
> 
> 
> cleanEx(); ..nameEx <- "wle.onestep"
> 
> ### * wle.onestep
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.onestep
> ### Title: A One-Step Weighted Likelihood Estimator for Linear model
> ### Aliases: wle.onestep
> ### Keywords: robust regression
> 
> ### ** Examples
> 
> #library(wle)
> #library(lqs)
> 
> #data(artificial)
> 
> #result.lts <- lqs(y.artificial~x.artificial, 
> #                 method = "lts")
> 
> #result.wle <- wle.onestep(y.artificial~x.artificial,
> #               ini.param=result.lts$coefficients,
> #               ini.scale=result.lts$scale[1])
> 
> #result.wle
> 
> 
> 
> cleanEx(); ..nameEx <- "wle.poisson"
> 
> ### * wle.poisson
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.poisson
> ### Title: Robust Estimation in the Poisson Model
> ### Aliases: wle.poisson print.wle.poisson
> ### Keywords: models robust
> 
> ### ** Examples
> 
> library(wle)
> 
> set.seed(1234)
> 
> x <- rpois(40,5)
> wle.poisson(x)

Call:
wle.poisson(x = x)

lambda:
[1]  4.731


Number of solutions  1 

> 
> x <- c(rpois(40,5),rpois(10,20))
> wle.poisson(x)

Call:
wle.poisson(x = x)

lambda:
[1]  4.509


Number of solutions  1 

> 
> 
> 
> 
> cleanEx(); ..nameEx <- "wle.smooth"
> 
> ### * wle.smooth
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.smooth
> ### Title: Bandwidth selection for the normal kernel and normal model.
> ### Aliases: wle.smooth print.wle.smooth
> ### Keywords: robust
> 
> ### ** Examples
> 
> library(wle)
> 
> wle.smooth()

Call:
wle.smooth()


Bandwidth:  0.003111
> 
> 
> 
> cleanEx(); ..nameEx <- "wle.stepwise"
> 
> ### * wle.stepwise
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.stepwise
> ### Title: Weighted Stepwise, Backward and Forward selection methods
> ### Aliases: wle.stepwise
> ### Keywords: robust regression
> 
> ### ** Examples
> 
> 
> library(wle)
> 
> # You can find this dataset in:
> # Agostinelli, C., (2002). Robust model selection in regression 
> # via weighted likelihood methodology, Statistics & 
> # Probability Letters, 56, 289-300.
> 
> data(selection)
> 
> result <- wle.stepwise(ydata~xdata, boot=100, group=6, num.sol=3,
+ min.weight=0.8, type="Stepwise", method="WLS")
> 
> summary(result)

Call:
wle.stepwise(formula = ydata ~ xdata, boot = 100, group = 6, 
    num.sol = 3, min.weight = 0.8, type = "Stepwise", method = "WLS")


 Stepwise  selection procedure

F.in:  4
F.out:  4 

Last  1  iterations:
(Intercept)      xdataX    xdataX^2             
          0           0           0           0 

> 
> 
> 
> cleanEx(); ..nameEx <- "wle.t.test"
> 
> ### * wle.t.test
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.t.test
> ### Title: Weighted Likelihood Student's t-Test
> ### Aliases: wle.t.test print.wle.t.test
> ### Keywords: robust htest
> 
> ### ** Examples
> 
> library(wle)
> 
> set.seed(1234)
> 
> x <- rnorm(20,0,1)
> y <- rnorm(20,6,1)
> 
> t.test(x,y)                # P < 2.2e-16

	Welch Two Sample t-test

data:  x and y 
t = -19.7269, df = 35.889, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -6.256951 -5.090237 
sample estimates:
 mean of x  mean of y 
-0.2506641  5.4229301 

> wle.t.test(x,y,group=5)    # P < 2.2e-16

Call:
wle.t.test(x = x, y = y, group = 5)



Weighted t test:

'x' Root  1 'y' Root  1
	Welch Two Sample wt-test for normal distributed data

data:  x and y 
wt = -23.8105, df = 30.758, p-value = < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -6.223333 -5.241027 
sample estimates:
[1] -0.3404375  5.3917426


Number of 'x' solutions  1 

Number of 'y' solutions  1 

> 
> t.test(x,y=c(y,250))       # P = 0.1419 -- NOT significant anymore

	Welch Two Sample t-test

data:  x and c(y, 250) 
t = -1.4867, df = 20.015, p-value = 0.1527
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -41.620311   6.980069 
sample estimates:
 mean of x  mean of y 
-0.2506641 17.0694572 

> wle.t.test(x,y=c(y,250),group=5) # P < 2.2e-16 -- still significant 

Call:
wle.t.test(x = x, y = c(y, 250), group = 5)



Weighted t test:

'x' Root  1 'y' Root  1
	Welch Two Sample wt-test for normal distributed data

data:  x and c(y, 250) 
wt = -23.842, df = 30.917, p-value = < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -6.223823 -5.242825 
sample estimates:
[1] -0.3404385  5.3928853


Number of 'x' solutions  1 

Number of 'y' solutions  1 

> set.seed(1234)
> 
> # three roots for 'x' and three roots for 'y'
> # with nine t-test value
> res <- wle.t.test(x=c(rnorm(40,0,1),rnorm(40,10,1)),
+            y=c(rnorm(40,0,1),rnorm(40,10,1)),
+            group=4,num.sol=3,boot=100)
> 
> print(res) # print ALL the t-test

Call:
wle.t.test(x = c(rnorm(40, 0, 1), rnorm(40, 10, 1)), y = c(rnorm(40, 
    0, 1), rnorm(40, 10, 1)), boot = 100, group = 4, num.sol = 3)



Weighted t test:

'x' Root  1 'y' Root  1
	Welch Two Sample wt-test for normal distributed data

data:  c(rnorm(40, 0, 1), rnorm(40, 10, 1)) and c(rnorm(40, 0, 1), rnorm(40, 10, 1)) 
wt = -0.3382, df = 123.042, p-value = 0.7358
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -0.5545859  0.3927116 
sample estimates:
[1] 5.028074 5.342190


'x' Root  1 'y' Root  2
	Welch Two Sample wt-test for normal distributed data

data:  c(rnorm(40, 0, 1), rnorm(40, 10, 1)) and c(rnorm(40, 0, 1), rnorm(40, 10, 1)) 
wt = 7.3451, df = 65.967, p-value = 3.94e-10
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 1.279824 2.235330 
sample estimates:
[1] -0.4877765  5.3421904


'x' Root  1 'y' Root  3
	Welch Two Sample wt-test for normal distributed data

data:  c(rnorm(40, 0, 1), rnorm(40, 10, 1)) and c(rnorm(40, 0, 1), rnorm(40, 10, 1)) 
wt = -7.2909, df = 68.406, p-value = 4.111e-10
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -2.222049 -1.267179 
sample estimates:
[1] 9.903944 5.342190


'x' Root  2 'y' Root  1
	Welch Two Sample wt-test for normal distributed data

data:  c(rnorm(40, 0, 1), rnorm(40, 10, 1)) and c(rnorm(40, 0, 1), rnorm(40, 10, 1)) 
wt = -8.8572, df = 67.628, p-value = 6.392e-13
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -2.596932 -1.641865 
sample estimates:
[1] -0.4877765  5.3421904


'x' Root  2 'y' Root  2
	Welch Two Sample wt-test for normal distributed data

data:  c(rnorm(40, 0, 1), rnorm(40, 10, 1)) and c(rnorm(40, 0, 1), rnorm(40, 10, 1)) 
wt = -2.6243, df = 65.758, p-value = 0.01079
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -1.1057280 -0.1501658 
sample estimates:
[1] -0.48777650  0.01481665


'x' Root  2 'y' Root  3
	Welch Two Sample wt-test for normal distributed data

data:  c(rnorm(40, 0, 1), rnorm(40, 10, 1)) and c(rnorm(40, 0, 1), rnorm(40, 10, 1)) 
wt = -49.1517, df = 67.45, p-value = < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -12.23883 -11.28372 
sample estimates:
[1] 9.90394422 0.01481665


'x' Root  3 'y' Root  1
	Welch Two Sample wt-test for normal distributed data

data:  c(rnorm(40, 0, 1), rnorm(40, 10, 1)) and c(rnorm(40, 0, 1), rnorm(40, 10, 1)) 
wt = 6.8421, df = 70.796, p-value = 2.311e-09
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 1.160076 2.114366 
sample estimates:
[1] 9.903944 5.342190


'x' Root  3 'y' Root  2
	Welch Two Sample wt-test for normal distributed data

data:  c(rnorm(40, 0, 1), rnorm(40, 10, 1)) and c(rnorm(40, 0, 1), rnorm(40, 10, 1)) 
wt = 45.1665, df = 64.112, p-value = < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 10.32967 11.28569 
sample estimates:
[1] 9.90394422 0.01481665


'x' Root  3 'y' Root  3
	Welch Two Sample wt-test for normal distributed data

data:  c(rnorm(40, 0, 1), rnorm(40, 10, 1)) and c(rnorm(40, 0, 1), rnorm(40, 10, 1)) 
wt = -0.6266, df = 70.12, p-value = 0.5329
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -0.6271653  0.3272845 
sample estimates:
[1]  9.903944 10.053885


Number of 'x' solutions  3 

Number of 'y' solutions  3 

> print(res,x.root=1,y.root=1)   # print the test associated to the 

Call:
wle.t.test(x = c(rnorm(40, 0, 1), rnorm(40, 10, 1)), y = c(rnorm(40, 
    0, 1), rnorm(40, 10, 1)), boot = 100, group = 4, num.sol = 3)



Weighted t test:

'x' Root  1 'y' Root  1
	Welch Two Sample wt-test for normal distributed data

data:  c(rnorm(40, 0, 1), rnorm(40, 10, 1)) and c(rnorm(40, 0, 1), rnorm(40, 10, 1)) 
wt = -0.3382, df = 123.042, p-value = 0.7358
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -0.5545859  0.3927116 
sample estimates:
[1] 5.028074 5.342190


Number of 'x' solutions  3 

Number of 'y' solutions  3 

>                                # x.root=1,y.root=1 
> 
> root.1.1 <- res$test[[1]][[1]] # access to the object associated 
>                                # to the x.root=1,y.root=1 
> 
> names(root.1.1)
 [1] "statistic"   "parameter"   "p.value"     "conf.int"    "estimate"   
 [6] "null.value"  "alternative" "method"      "data.name"   "x.weights"  
[11] "y.weights"   "x.root"      "y.root"     
> 
> set.seed(1234)
> 
> # one root and NOT significant t-test
> wle.t.test(x=c(rnorm(40,0,1),rnorm(40,10,1)),
+            y=c(rnorm(40,0,1),rnorm(40,10,1)),
+            group=4,num.sol=3,boot=100,paired=TRUE)

Call:
wle.t.test(x = c(rnorm(40, 0, 1), rnorm(40, 10, 1)), y = c(rnorm(40, 
    0, 1), rnorm(40, 10, 1)), paired = TRUE, boot = 100, group = 4, 
    num.sol = 3)



Weighted t test:

'x' Root  1
	Paired wt-test for normal distributed data

data:  c(rnorm(40, 0, 1), rnorm(40, 10, 1)) and c(rnorm(40, 0, 1), rnorm(40, 10, 1)) 
wt = -2.0945, df = 74.02, p-value = 0.03964
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -0.55679572 -0.01389546 
sample estimates:
[1] -0.2853456


Number of 'x' solutions  1 

> 
> 
> 
> 
> cleanEx(); ..nameEx <- "wle.var.test"
> 
> ### * wle.var.test
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.var.test
> ### Title: Weighted F Test to Compare Two Variances
> ### Aliases: wle.var.test
> ### Keywords: robust htest
> 
> ### ** Examples
> 
> 
> set.seed(2345)
> 
> x <- rnorm(50,0,1)
> y <- rnorm(50,10,1)
> 
> res.x <- wle.normal(x,group=5)
> res.y <- wle.normal(y,group=5)
> 
> wle.var.test(res.x, res.y) # Do x and y have the same variance?

	WF test to compare two variances

data:  res.x and res.y 
WF = 0.6387, num df = 42.936, denom df = 45.386, p-value = 0.1419
alternative hypothesis: true ratio of variances is not equal to 1 
95 percent confidence interval:
 0.3521775 1.1641298 
sample estimates:
ratio of variances 
         0.6386964 

> 
> set.seed(2345)
> 
> x <- c(rnorm(50,0,1),rnorm(20,10,1))
> y <- c(rnorm(50,10,1),rnorm(10,0,5))
> 
> res.x <- wle.normal(x,group=5,num.sol=2)
> res.y <- wle.normal(y,group=5)
> 
> res.x

Call:
wle.normal(x = x, group = 5, num.sol = 2)

Location:
[1]   2.71327  -0.04928

Scale:
[1]  4.5264  0.8119


Number of solutions  2 

> wle.var.test(res.x, res.y, x.root=1)

	WF test to compare two variances

data:  res.x and res.y 
WF = 18.5957, num df = 52.963, denom df = 46.606, p-value < 2.2e-16
alternative hypothesis: true ratio of variances is not equal to 1 
95 percent confidence interval:
 10.53441 32.49160 
sample estimates:
ratio of variances 
          18.59568 

> if (res.x$tot.sol>1) wle.var.test(res.x, res.y, x.root=2)

	WF test to compare two variances

data:  res.x and res.y 
WF = 0.6006, num df = 43.755, denom df = 46.606, p-value = 0.09167
alternative hypothesis: true ratio of variances is not equal to 1 
95 percent confidence interval:
 0.3335395 1.0874394 
sample estimates:
ratio of variances 
         0.6005765 

> 
> 
> 
> cleanEx(); ..nameEx <- "wle.vonmises"
> 
> ### * wle.vonmises
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.vonmises
> ### Title: von Mises Weighted Likelihood Estimates
> ### Aliases: wle.vonmises print.wle.vonmises
> ### Keywords: robust
> 
> ### ** Examples
> 
> 
> if (require(circular)) {
+     x <- c(rvonmises(n=50, mu=0, kappa=10), rvonmises(n=5, mu=pi/2, kappa=20))
+     wle.vonmises(x, smooth=20, group=5)
+ } else {
+    cat("Please, install the package 'circular' in order to use this function.\n")
+ }
Loading required package: circular
Loading required package: boot
This is version 0.3-2 of circular package
Please report any bugs or comments to <Claudio Agostinelli> claudio@unive.it 
The package redefine how function 'var' works 
In particular, (try 'methods(var)') 
 notice that 'var.default' is an alias for the original 'var' function 
 and that a method for data.frame is available.

Attaching package: 'circular'


	The following object(s) are masked from package:stats :

	 var 


Call:
wle.vonmises(x = x, group = 5, smooth = 20)

mu:
[1]  -0.01395

kappa:
[1]  6.635


Number of solutions  1 

> 
> 
> 
> 
> cleanEx(); ..nameEx <- "wle.wrappednormal"
> 
> ### * wle.wrappednormal
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: wle.wrappednormal
> ### Title: Wrapped Normal Weighted Likelihood Estimates
> ### Aliases: wle.wrappednormal print.wle.wrappednormal
> ### Keywords: robust
> 
> ### ** Examples
> 
> 
> if (require(circular)) {
+     x <- c(rwrappednormal(n=50, mu=0, sd=1), rwrappednormal(n=5, mu=pi/2, sd=0.5))
+     wle.wrappednormal(x, smooth=1/20, group=5)
+ } else {
+    cat("Please, install the package 'circular' in order to use this function.\n")
+ }
Loading required package: circular
Loading required package: boot
This is version 0.3-2 of circular package
Please report any bugs or comments to <Claudio Agostinelli> claudio@unive.it 
The package redefine how function 'var' works 
In particular, (try 'methods(var)') 
 notice that 'var.default' is an alias for the original 'var' function 
 and that a method for data.frame is available.

Attaching package: 'circular'


	The following object(s) are masked from package:stats :

	 var 


Call:
wle.wrappednormal(x = x, group = 5, smooth = 1/20)

mu:
0.2584 

rho: 0.6765 

sd: 0.884 


Number of solutions  1 

> 
> 
> 
> 
> ### * <FOOTER>
> ###
> cat("Time elapsed: ", proc.time() - get("ptime", env = .CheckExEnv),"\n")
Time elapsed:  40.55 0.33 41.11 0 0 
> grDevices::dev.off()
null device 
          1 
> ###
> ### Local variables: ***
> ### mode: outline-minor ***
> ### outline-regexp: "\\(> \\)?### [*]+" ***
> ### End: ***
> quit('no')