Domean (version 0.1)

covclx: Two-Sample Covariance Test for High-Dimensional Data

Description

Performs a test to compare the covariance matrices of two high-dimensional samples. This test is designed for situations where the number of variables \( p \) is large relative to the sample sizes \( n_1 \) and \( n_2 \).

Usage

covclx(X, Y)

Value

A list containing the following components:

stat

The test statistic.

pval

The p-value of the test.

Arguments

X

A numeric matrix representing the first sample, where rows are observations and columns are variables.

Y

A numeric matrix representing the second sample, where rows are observations and columns are variables.

Details

This function tests the null hypothesis that the covariance matrices of two samples are equal: $$H_0: \Sigma_1 = \Sigma_2$$ against the alternative hypothesis that they are not equal.

The test statistic is based on the maximum normalized squared difference between the two sample covariance matrices. The p-value is computed using an extreme value distribution.

See Also

cov: Used for calculating sample covariance matrices.

Examples

  # Example usage:
  set.seed(123)
  n1 <- 20
  n2 <- 30
  p <- 50
  X <- matrix(rnorm(n1 * p), nrow = n1, ncol = p)
  Y <- matrix(rnorm(n2 * p), nrow = n2, ncol = p)
  result <- covclx(X, Y)
  print(result)