High-dimensional asymptotic behavior of the difference between the log-determinants of two Wishart matrices

JOURNAL OF MULTIVARIATE ANALYSIS

卷:157

Article

Yanagihara, Hirokazu^1,2  Oda, Ryoya¹  Hashiyama, Yusuke^1,3  Fujikoshi, Yasunori^1,2 

[1] Hiroshima Univ, Grad Sch Sci, Dept Math, 1-3-1 Kagamiyama, Higashihiroshima 7398626, Japan

[2] Hiroshima Univ, Stat Sci Res Core, 1-3-1 Kagamiyama, Higashihiroshima, Hiroshima 7398626, Japan

[3] Osaka Prefectural Ibaraki High Sch, 12-1 Shinjo Cho, Ibaraki, Osaka 5670884, Japan

关键词: Canonical correlation analysis;    Consistency of information criterion;    High-dimensional asymptotic framework;    Information criterion;    Model selection;   

DOI  :  10.1016/j.jmva.2017.03.002

来源: Elsevier

【 摘 要 】

In this paper, we evaluate the asymptotic behavior of the difference between the log determinants of two random matrices distributed according to the Wishart distribution by using a high-dimensional asymptotic framework in which the size of the matrices and the degrees of freedom both approach infinity simultaneously. We consider two cases, depending whether a matrix is completely or partially included in another matrix. From the asymptotic behavior, we derive the condition needed to ensure consistency for a given log-likelihood-based information criterion for selecting variables in a canonical correlation analysis. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free