| ind.ictest {ICSNP} | R Documentation |
Performs the test that a group of variables is independent of an other based on marginal ranks. It is assumed that the data follows a symmetric IC model. Three different score functions are available.
ind.ictest(X, index1, index2 = NULL, scores = "rank",
method = "approximation", n.simu = 1000,
..., na.action = na.fail)
X |
a data frame or matrix. |
index1 |
integer vector that selects the columns of X that form group one. Only numeric columns can be selected. |
index2 |
integer vector that selects the columns of X that form group two. Only numeric columns can be selected.
If NULL, all remaining columns of X will be selected. |
scores |
if 'sign', a sign test is performed, if 'rank' a signed rank test is performed or if 'normal' a normal score test is performed. |
method |
defines the method used for the computation of the p-value. The possobilites are "approximation" (default), "simulation" or "permutation". Details below. |
n.simu |
if 'method=simulation' or 'method=permutation' this specifies the number of replications usedin the
simulation or permutation procedure. |
... |
further arguments to be passed to the function ics |
na.action |
a function which indicates what should happen when the data contain 'NA's. Default is to fail. |
Assumed is here that X[ , index1] comes from a symmetric independent component model which in turn is independent from X[ , index2] which has also
an underlying symmetric independent component model. This function recovers the independent components using the function ics, centers them by their marginal
medians and performs then the test as described in Oja, Paindaveine and Taskinen (2007).
The asymptotic chi-square distibution is however even for large sample sizes inadequat and therefore p-values can be simulated by resampling the test statistic under the null
hypothesis or by permuting the rows of the independent components of X[ , index2]. Both alternatives are also described in Oja, Paindaveine and Taskinen (2007).
A list with class 'htest' containing the following components:
statistic |
the value of the Q-statistic. |
parameter |
the degrees of freedom for the Q-statistic or the number of replications depending on the chosen method. |
p.value |
the p-value for the test. |
method |
a character string indicating what type of test was performed. |
data.name |
a character string giving the name of the data. |
Klaus Nordhausen, klaus.nordhausen@uta.fi
Oja, H. and Paindaveine, D. and Taskinen, S. (2007), Parametric and Nonparametric Test for Multivariate Independence in IC Models, Manuscript, 1, 1–23.
Z1<-cbind(rt(500,5),rnorm(500),runif(500)) Z2<-cbind(rt(500,8),rbeta(500,2,2)) A1 <- matrix(c(4, 4, 5, 4, 6, 6, 5, 6, 7), ncol = 3) A2 <- matrix(c(0.5, -0.3, -0.3, 0.7), ncol = 2) X <- cbind(Z1 %*% t(A1), Z2 %*% t(A2)) ind.ictest(X,1:3) ind.ictest(X,1:3,method="simu") ind.ictest(X,1:2,3:5,method="perm", S1=tyler.shape,S2=cov)