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PECO: Two-Sample Covariance Test by Yu, Li, Xue and Li(2022)

Description

Given two sets of data matrices X and Y, where X is an n1 rows and p cols matrix and Y is an n2 rows and p cols matrix, we conduct hypothesis testing of the covariance matrix between two samples. The null hypothesis is: $$H_0 : \Sigma_1 = \Sigma_2$$ \(\Sigma_1\) and \(\Sigma_2\) are the sample covariance matrices of X and Y respectively. This test method is based on the test method proposed by Yu, Li, Xue and Li (2022). When the pval value is less than the significance coefficient (generally 0.05), the null hypothesis is rejected.

Usage

PECO(X,Y,delta = NULL)

Value

stat

a test statistic value.

pval

a test p_value.

Arguments

X

A matrix of n1 by p

Y

A matrix of n2 by p

delta

A scalar used as the threshold for building PE components, usually the default value.

References

Yu, X., Li, D., Xue, L., and Li, R. (2022). Power-enhanced simultaneous test of high-dimensional mean vectors and covariance matrices with application to gene-set testing. Journal of the American Statistical Association, (in press):1-14.

Examples

## generate X and Y.
p= 500;  n1 = 100; n2 = 150
X=matrix(rnorm(n1*p), ncol=p)
Y=matrix(rnorm(n2*p), ncol=p)
## run test
PECO(X,Y)