cmtwo: Two-Sample Covariance Test by Cai and Ma (2013)

In Docovt: Distributed Online Covariance Matrix Tests

Two-Sample Covariance Test by Cai and Ma (2013)

Description

Given two sets of data, it performs 2-sample test for equality of covariance matrices where the null hypothesis is

H_0 : \Sigma_1 = \Sigma_2

where \Sigma_1 and \Sigma_2 represent true (unknown) covariance for each dataset based on a procedure proposed by Cai and Ma (2013). If statistic > threshold, it rejects null hypothesis.

Usage

cmtwo(X, Y, alpha)

Arguments

X	an (m\times p) matrix where each row is an observation from the first dataset.
Y	an (n\times p) matrix where each row is an observation from the second dataset.
alpha	level of significance.

Value

a named list containing

statistic

a test statistic value.

threshold

rejection criterion to be compared against test statistic.

reject

a logical; TRUE to reject null hypothesis, FALSE otherwise.

Examples

## generate 2 datasets from multivariate normal with identical covariance.
p= 5;  n1 = 100; n2 = 150; alpha=0.05
X=data1 = matrix(rnorm(n1*p), ncol=p)
Y=data2 = matrix(rnorm(n2*p), ncol=p)

# run test
cmtwo(X, Y, alpha)

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