mean1.2008SD {SHT}

One-sample Test for Mean Vector by Srivastava and Du (2008)

Description

Given a multivariate sample X and hypothesized mean \mu_0, it tests

H_0 : \mu_x = \mu_0\quad vs\quad H_1 : \mu_x \neq \mu_0

using the procedure by Srivastava and Du (2008).

Usage

mean1.2008SD(X, mu0 = rep(0, ncol(X)))

Arguments

X

an (n\times p) data matrix where each row is an observation.

mu0

a length-p mean vector of interest.

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

Srivastava MS, Du M (2008). “A test for the mean vector with fewer observations than the dimension.” Journal of Multivariate Analysis, 99(3), 386–402. ISSN 0047259X.

Examples

## CRAN-purpose small example
smallX = matrix(rnorm(10*3),ncol=3)
mean1.2008SD(smallX) # run the test


## empirical Type 1 error 
niter   = 1000
counter = rep(0,niter)  # record p-values
for (i in 1:niter){
  X = matrix(rnorm(50*5), ncol=5)
  counter[i] = ifelse(mean1.2008SD(X)$p.value < 0.05, 1, 0)
}

## print the result
cat(paste("\n* Example for 'mean1.2008SD'\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=""))