CovTools (version 0.5.4)

CovTest1.2013Cai: 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_optimal_2013CovTools

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)
# }
# NOT RUN {
# }