meank.2007Schott {SHT}

Test for Equality of Means by Schott (2007)

Description

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

H_0 : \mu_1 = \cdots \mu_k\quad vs\quad H_1 : \textrm{at least one equality does not hold}

using the procedure by Schott (2007). It can be considered as a generalization of two-sample testing procedure proposed by Bai and Saranadasa (1996).

Usage

meank.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). “Some high-dimensional tests for a one-way MANOVA.” Journal of Multivariate Analysis, 98(9), 1825–1839. ISSN 0047259X.

Examples

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


## test when k=5 samples with (n,p) = (10,50)
## empirical Type 1 error 
niter   = 1000
counter = rep(0,niter)  # record p-values
for (i in 1:niter){
  mylist = list()
  for (j in 1:5){
     mylist[[j]] = matrix(rnorm(10*5),ncol=5)
  }
  
  counter[i] = ifelse(meank.2007Schott(mylist)$p.value < 0.05, 1, 0)
}

## print the result
cat(paste("\n* Example for 'meank.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=""))