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

Hirokazu Yanagihara, Ryoya Oda, Yusuke Hashiyama and Yasunori Fujikoshi

Journal of Multivariate Analysis, 2017, vol. 157, issue C, 70-86

Abstract: 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.

Keywords: Canonical correlation analysis; Consistency of information criterion; High-dimensional asymptotic framework; Information criterion; Model selection (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.jmva.2017.03.002

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