Title

Tests For Kronecker Envelope Models In Multilinear Principal Components Analysis

Keywords

Asymptotic null distribution; Likelihood ratio test; Saddlepoint approximation

Abstract

We develop likelihood methods for the Kronecker envelope model in the principal components analysis of matrix observations that have a multivariate normal distribution. Maximum likelihood estimates are derived and the associated likelihood ratio statistic for a test of this Knonecker envelope model is obtained. The asymptotic null distribution of the likelihood ratio statistic is derived as some nuisance parameters approach infinity, and a saddlepoint approximation for this limiting distribution is given. An alternative composite test for the Kronecker envelope model, which can be used when the sample size is too small to use the likelihood ratio test, is also given. Simulation results demonstrate the accuracy of our approximations.

Publication Date

12-1-2014

Publication Title

Biometrika

Volume

101

Issue

4

Number of Pages

978-984

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1093/biomet/asu029

Socpus ID

84985920456 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84985920456

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