covk.2007Schott {SHT}

Test for Homogeneity of Covariances by Schott (2007)

Description

Given univariate samples X_1~,\ldots,~X_k, it tests

H_0 : \Sigma_1 = \cdots \Sigma_k\quad vs\quad H_1 : \textrm{at least one equality does not hold}

using the procedure by Schott (2007).

Usage

covk.2007Schott(dlist)

Arguments

dlist

a list of length k where each element is a sample matrix of same dimension.

Value

a (list) object of S3 class htest containing:

statistic

a test statistic.

p.value

p-value under H_0.

alternative

alternative hypothesis.

method

name of the test.

data.name

name(s) of provided sample data.

References

Schott JR (2007). “A test for the equality of covariance matrices when the dimension is large relative to the sample sizes.” Computational Statistics & Data Analysis, 51(12), 6535–6542. ISSN 01679473.

Examples

## CRAN-purpose small example
tinylist = list()
for (i in 1:3){ # consider 3-sample case
  tinylist[[i]] = matrix(rnorm(10*3),ncol=3)
}
covk.2007Schott(tinylist) # run the test


## test when k=4 samples with (n,p) = (100,20)
## empirical Type 1 error 
niter   = 1234
counter = rep(0,niter)  # record p-values
for (i in 1:niter){
  mylist = list()
  for (j in 1:4){
     mylist[[j]] = matrix(rnorm(100*20),ncol=20)
  }
  
  counter[i] = ifelse(covk.2007Schott(mylist)$p.value < 0.05, 1, 0)
}

## print the result
cat(paste("\n* Example for 'covk.2007Schott'\n","*\n",
"* number of rejections   : ", sum(counter),"\n",
"* total number of trials : ", niter,"\n",
"* empirical Type 1 error : ",round(sum(counter/niter),5),"\n",sep=""))