CovTest {RMT4DS}

High-dimensional Covariance Test

Description

Test of given population covariance matrix, test of equal covariance of two or more samples.

Usage

OneSampleCovTest(X, mean=NULL, S=NULL)
TwoSampleCovTest(X1, X2, mean=NULL)
MultiSampleCovTest(..., input=NULL)

Arguments

X, X1, X2

input samples in the form n by p where p is the dimension.

mean

population mean of samples. If it is missing, sample mean will be used.

S

covariance matrix to be tested. If it is missing, test of identity covariance will be performed.

...

any samples to be tested.

input

list of samples to be tested. Please choose either ... or input as input form.

Value

OneSampleCovTest tests given covariance matrix of one sample,

TwoSampleCovTest tests equal covariance matrices of two samples,

MultiSampleCovTest tests equal covariance matrices of multiple samples.

Author(s)

Xiucai Ding, Yichen Hu

Source

Maximal likelihood tests fail in high-dimensional settings, so corrections are made. Note all tests are one-sided. Large statistics indicate violation of null hypothesis.

References

[1] Zheng, S., Bai, Z., & Yao, J. (2015). Substitution principle for CLT of linear spectral statistics of high-dimensional sample covariance matrices with applications to hypothesis testing. The Annals of Statistics, 43(2), 546-591.

Examples

require(MASS)
n = 500
p = 100
S1 = diag(rep(1,p))
S2 = diag(sample(c(1,4),p,replace=TRUE))
OneSampleCovTest(mvrnorm(n,rep(0,p),S2), S=S1)
TwoSampleCovTest(mvrnorm(n,rep(0,p),S1), mvrnorm(n,rep(0,p),S2))
MultiSampleCovTest(mvrnorm(n,rep(0,p),S1), mvrnorm(n,rep(0,p),S2))