Tests for Kronecker envelope models in multilinear principal components analysis
成果类型：
Article
署名作者：
Schott, James R.
署名单位：
State University System of Florida; University of Central Florida
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/asu029
发表日期：
2014
页码：
978984
关键词：
摘要：
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.