| wle.normal.multi {wle} | R Documentation |
wle.normal.multi is used to robust estimate the location and the covariance matrix via Weighted Likelihood, when the sample is iid from a normal multivariate distribution with unknown means and variance matrix.
wle.normal.multi(x, boot=30, group, num.sol=1,
raf="HD", smooth, tol=10^(-6),
equal=10^(-3), max.iter=500,
verbose=FALSE)
x |
a matrix contain the observations. |
boot |
the number of starting points based on boostrap subsamples to use in the search of the roots. |
group |
the dimension of the bootstap subsamples. The default value is max(round(size/4),(var*(var+1)/2+var)) where size is the number of observations and var is the number of variables. |
num.sol |
maximum number of roots to be searched. |
raf |
type of Residual adjustment function to be use:
raf="HD": Hellinger Distance RAF,
raf="NED": Negative Exponential Disparity RAF,
raf="SCHI2": Symmetric Chi-Squared Disparity RAF. |
smooth |
the value of the smoothing parameter. |
tol |
the absolute accuracy to be used to achieve convergence of the algorithm. |
equal |
the absolute value for which two roots are considered the same. (This parameter must be greater than tol). |
max.iter |
maximum number of iterations. |
verbose |
if TRUE warnings are printed. |
wle.normal.multi returns an object of class "wle.normal.multi".
Only print method is implemented for this class.
The object returned by wle.normal.multi are:
location |
the estimator of the location parameters, one vector for each root found. |
variance |
the estimator of the covariance matrix, one matrix for each root found. |
tot.weights |
the sum of the weights divide by the number of observations, one value for each root found. |
weights |
the weights associated to each observation, one column vector for each root found. |
f.density |
the non-parametric density estimation. |
m.density |
the smoothed model. |
delta |
the Pearson residuals. |
freq |
the number of starting points converging to the roots. |
tot.sol |
the number of solutions found. |
call |
the match.call(). |
not.conv |
the number of starting points that does not converge after the max.iter iteration are reached. |
Claudio Agostinelli
Markatou, M., Basu, A. and Lindsay, B.G., (1998) Weighted likelihood estimating equations with a bootstrap root search, Journal of the American Statistical Association, 93, 740-750.
Agostinelli, C., (1998) Inferenza statistica robusta basata sulla funzione di verosimiglianza pesata: alcuni sviluppi, Ph.D Thesis, Department of Statistics, University of Padova.
wle.smooth an algorithm to choose the smoothing parameter for normal distribution and normal kernel.
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$root)
result
result <- wle.normal.multi(x.data,boot=20,group=21,
num.sol=1,smooth=smooth$root)
barplot(result$weights,col=2,xlab="Observations",
ylab="Weights",ylim=c(0,1),
names.arg=seq(1:length(result$weights)))