Premium
Testing block‐diagonal covariance structure for high‐dimensional data
Author(s) -
Hyodo Masashi,
Shutoh Nobumichi,
Nishiyama Takahiro,
Pavlenko Tatjana
Publication year - 2015
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/stan.12068
Subject(s) - mathematics , test statistic , wishart distribution , covariance , statistics , statistic , estimator , covariance matrix , null distribution , estimation of covariance matrices , statistical hypothesis testing , asymptotic distribution , likelihood ratio test , consistency (knowledge bases) , multivariate statistics , discrete mathematics
A test statistic is developed for making inference about a block‐diagonal structure of the covariance matrix when the dimensionality p exceeds n , where n = N − 1 and N denotes the sample size. The suggested procedure extends the complete independence results. Because the classical hypothesis testing methods based on the likelihood ratio degenerate when p > n , the main idea is to turn instead to a distance function between the null and alternative hypotheses. The test statistic is then constructed using a consistent estimator of this function, where consistency is considered in an asymptotic framework that allows p to grow together with n . The suggested statistic is also shown to have an asymptotic normality under the null hypothesis. Some auxiliary results on the moments of products of multivariate normal random vectors and higher‐order moments of the Wishart matrices, which are important for our evaluation of the test statistic, are derived. We perform empirical power analysis for a number of alternative covariance structures.