Docovt (version 0.2)

cmtwo: 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)

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.

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.

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)