Docovt (version 0.2)

cm13: 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)

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 \((n\times p)\) data matrix where each row is an observation.

Sigma0

a \((p\times p)\) given covariance matrix.

alpha

level of significance.

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)