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

In Docovt: Distributed Online Covariance Matrix Tests

Two-Sample Covariance Test by Yu, Li and Xue (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 and Xue (2022). When the pval value is less than the significance coefficient (generally 0.05), the null hypothesis is rejected.

Usage

PEF(X,Y)

Arguments

X	A matrix of n1 by p
Y	A matrix of n2 by p

Value

stat	a test statistic value.
pval	a test p_value.

References

Yu, X., Li, D., and Xue, L. (2022). Fisher's combined probability test for high-dimensional covariance matrices. 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
PEF(X,Y)

Docovt documentation built on June 30, 2025, 9:07 a.m.