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

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  • Yanagihara, Hirokazu
  • Oda, Ryoya
  • Hashiyama, Yusuke
  • Fujikoshi, Yasunori

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.

Suggested Citation

  • Yanagihara, Hirokazu & Oda, Ryoya & Hashiyama, Yusuke & Fujikoshi, Yasunori, 2017. "High-dimensional asymptotic behavior of the difference between the log-determinants of two Wishart matrices," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 70-86.
    • Handle: RePEc:eee:jmvana:v:157:y:2017:i:c:p:70-86
    DOI: 10.1016/j.jmva.2017.03.002
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    References listed on IDEAS

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    1. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
    2. Fujikoshi, Yasunori & Sakurai, Tetsuro & Yanagihara, Hirokazu, 2014. "Consistency of high-dimensional AIC-type and Cp-type criteria in multivariate linear regression," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 184-200.
    3. Wakaki, Hirofumi, 2006. "Edgeworth expansion of Wilks' lambda statistic," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1958-1964, October.
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