DiagTest1.2011Cai {CovTools} | R Documentation |
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 |
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)