cm13: One-Sample Covariance Test by Cai and Ma (2013)

In Docovt: Distributed Online Covariance Matrix Tests

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

Description

Given data, it performs 1-sample test for Covariance where the null hypothesis is

H_0 : \Sigma_n = \Sigma_0

where \Sigma_n is the covariance of data model and \Sigma_0 is a hypothesized covariance based on a procedure proposed by Cai and Ma (2013).

Usage

cm13(X,Sigma0, alpha)

Arguments

X	an (n\times p) data matrix where each row is an observation.
Sigma0	a (p\times p) given covariance matrix.
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 data from multivariate normal with trivial covariance.
p = 5;n=10
X=data = matrix(rnorm(n*p), ncol=p)
alpha=0.05
Sigma0=diag(ncol(X))
cm13(X,Sigma0, alpha)

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