DiagTest1.2011Cai {CovTools}

One-Sample Diagonality Test by Cai and Jiang (2011)

Description

Given data, it performs 1-sample test for diagonal entries of a Covariance matrix where the null hypothesis is

H_0 : \sigma_{ij} = 0~\mathrm{for any}~i \neq j

and alternative hypothesis is H_1 : ~\mathrm{not}~H_0 with \Sigma_n = (\sigma_{ij}) based on a procedure proposed by Cai and Jiang (2011).

Usage

DiagTest1.2011Cai(data, alpha = 0.05)

Arguments

data

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

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, Jiang T (2011). “Limiting laws of coherence of random matrices with applications to testing covariance structure and construction of compressed sensing matrices.” The Annals of Statistics, 39(3), 1496–1525. ISSN 0090-5364.

Examples

## Not run: 
## generate data from multivariate normal with trivial covariance.
pdim = 5
data = matrix(rnorm(100*pdim), ncol=pdim)

## run test with different alpha values
DiagTest1.2011Cai(data, alpha=0.01)
DiagTest1.2011Cai(data, alpha=0.05)
DiagTest1.2011Cai(data, alpha=0.10)

## End(Not run)