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
Copyright Status
Unknown
Socpus ID
84985920456 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84985920456
STARS Citation
Schott, James R., "Tests For Kronecker Envelope Models In Multilinear Principal Components Analysis" (2014). Scopus Export 2010-2014. 8346.
https://stars.library.ucf.edu/scopus2010/8346