ind.ictest {ICSNP}R Documentation

Test of Independence based on Marginal Ranks in a Symmetric IC Model

Description

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.

Usage

ind.ictest(X, index1, index2 = NULL, scores = "rank", 
           method = "approximation", n.simu = 1000, 
           ..., na.action = na.fail)

Arguments

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 used in 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.

Details

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).

Value

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.

Author(s)

Klaus Nordhausen, klaus.nordhausen@uta.fi

References

Oja, H. and Paindaveine, D. and Taskinen, S. (2007), Parametric and Nonparametric Test for Multivariate Independence in IC Models, Manuscript, 1, 1–23.

Examples

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)


[Package ICSNP version 1.0-2 Index]