# sim1.LRT: One-sample Simultaneous Likelihood Ratio Test of Mean and... In SHT: Statistical Hypothesis Testing Toolbox

 sim1.LRT R Documentation

## One-sample Simultaneous Likelihood Ratio Test of Mean and Covariance

### Description

Given a multivariate sample X, hypothesized mean μ_0 and covariance Σ_0, it tests

H_0 : μ_x = μ_0 \textrm{ and } Σ_x = Σ_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)



SHT documentation built on Nov. 3, 2022, 9:06 a.m.