sim1.LRT {SHT}

One-sample Simultaneous Likelihood Ratio Test of Mean and Covariance

Description

Given a multivariate sample X, hypothesized mean \mu_0 and covariance \Sigma_0, it tests

H_0 : \mu_x = \mu_0 \textrm{ and } \Sigma_x = \Sigma_0 \quad vs\quad H_1 : \textrm{ not } H_0

using the standard likelihood-ratio test procedure.

Usage

sim1.LRT(X, mu0 = rep(0, ncol(X)), Sigma0 = diag(ncol(X)))

Arguments

X

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

mu0

a length-p mean vector of interest.

Sigma0

a (p\times p) given covariance matrix.

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.

Examples

## CRAN-purpose small example
smallX = matrix(rnorm(10*3),ncol=3)
sim1.LRT(smallX) # run the test

## Not run: 
## empirical Type 1 error 
niter   = 1000
counter = rep(0,niter)  # record p-values
for (i in 1:niter){
  X = matrix(rnorm(100*10), ncol=10)
  counter[i] = ifelse(sim1.LRT(X)$p.value < 0.05, 1, 0)
  print(paste("* iteration ",i,"/1000 complete..."))
}

## print the result
cat(paste("\n* Example for 'sim1.LRT'\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=""))

## End(Not run)