DiagTest1.2011Cai {CovTools} | R Documentation |
Given data, it performs 1-sample test for diagonal entries of a Covariance matrix where the null hypothesis is
H_0 : σ_{ij} = 0~\mathrm{for any}~i \neq j
and alternative hypothesis is H_1 : ~\mathrm{not}~H_0 with Σ_n = (σ_{ij}) based on a procedure proposed by Cai and Jiang (2011).
DiagTest1.2011Cai(data, alpha = 0.05)
data |
an (n\times p) data matrix where each row is an observation. |
alpha |
level of significance. |
a named list containing:
a test statistic value.
rejection criterion to be compared against test statistic.
a logical; TRUE
to reject null hypothesis, FALSE
otherwise.
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.
## 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)