CovTest1.2013Cai {CovTools}

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

CovTest1.2013Cai(data, Sigma0 = diag(ncol(data)), alpha = 0.05)

Arguments

data

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.

References

Cai TT, Ma Z (2013). “Optimal hypothesis testing for high dimensional covariance matrices.” Bernoulli, 19(5B), 2359–2388. ISSN 1350-7265.

Examples

## Not run: 
## generate data from multivariate normal with trivial covariance.
pdim = 5
data = matrix(rnorm(10*pdim), ncol=pdim)

## run the test
CovTest1.2013Cai(data)

## End(Not run)