CovTools (version 0.2.1)

CovTest1: One-Sample Tests for Covariance Matrices

Description

Given data, CovTest1 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.

Usage

CovTest1(data, Sigma0 = diag(ncol(data)), alpha = 0.05,
  method = c("Cai13"))

Arguments

data

an (n-by-p) data matrix where each row is an observation.

Sigma0

a (p-by-p) given covariance matrix.

alpha

level of significance.

method

a name of test.

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

[Cai13] Cai, T. and Ma, Z. (2013) Optimal hypothesis testing for high dimensional covariance matrices. Bernoulli, Vol.19(5B):2359-2388.

Examples

# NOT RUN {
## generate data from multivariate normal with trivial covariance.
data = mvtnorm::rmvnorm(100, sigma=diag(5))

## run test
CovTest1(data, Sigma0=diag(5))

# }