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Testing block-diagonal covariance structure for high-dimensional data
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2015 (English)In: Statistica neerlandica (Print), ISSN 0039-0402, E-ISSN 1467-9574, Vol. 69, no 4, 460-482 p.Article in journal (Refereed) PublishedText
Abstract [en]

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.

Place, publisher, year, edition, pages
Wiley-Blackwell, 2015. Vol. 69, no 4, 460-482 p.
Keyword [en]
Block-diagonal covariance structure, High dimensionality
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-181237DOI: 10.1111/stan.12068ISI: 000362911600007ScopusID: 2-s2.0-84944157510OAI: oai:DiVA.org:kth-181237DiVA: diva2:901809
Note

QC 20160209

Available from: 2016-02-09 Created: 2016-01-29 Last updated: 2016-02-09Bibliographically approved

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Pavlenko, Tetyana
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