sim1.2017Liu {SHT}

One-sample Simultaneous Test of Mean and Covariance by Liu et al. (2017)

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 procedure by Liu et al. (2017).

Usage

sim1.2017Liu(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.

References

Liu Z, Liu B, Zheng S, Shi N (2017). “Simultaneous testing of mean vector and covariance matrix for high-dimensional data.” Journal of Statistical Planning and Inference, 188, 82–93. ISSN 03783758.

Examples

## CRAN-purpose small example
smallX = matrix(rnorm(10*3),ncol=3)
sim1.2017Liu(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(50*10), ncol=10)
  counter[i] = ifelse(sim1.2017Liu(X)$p.value < 0.05, 1, 0)
}

## print the result
cat(paste("\n* Example for 'sim1.2017Liu'\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)