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Strong Consistency of Log-Likelihood-Based Information Criterion in High-Dimensional Canonical Correlation Analysis

Author

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  • Ryoya Oda

    (Hiroshima University)

  • Hirokazu Yanagihara

    (Hiroshima University)

  • Yasunori Fujikoshi

    (Hiroshima University)

Abstract

We consider the strong consistency of a log-likelihood-based information criterion in a normality-assumed canonical correlation analysis between q- and p-dimensional random vectors for a high-dimensional case such that the sample size n and number of dimensions p are large but p/n is less than 1. In general, strong consistency is a stricter property than weak consistency; thus, sufficient conditions for the former do not always coincide with those for the latter. We derive the sufficient conditions for the strong consistency of this log-likelihood-based information criterion for the high-dimensional case. It is shown that the sufficient conditions for strong consistency of several criteria are the same as those for weak consistency obtained by Yanagihara et al. (J. Multivariate Anal. 157, 70–86: 2017).

Suggested Citation

  • Ryoya Oda & Hirokazu Yanagihara & Yasunori Fujikoshi, 2021. "Strong Consistency of Log-Likelihood-Based Information Criterion in High-Dimensional Canonical Correlation Analysis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 109-127, February.
    • Handle: RePEc:spr:sankha:v:83:y:2021:i:1:d:10.1007_s13171-019-00174-3
    DOI: 10.1007/s13171-019-00174-3
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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. Ogura, Toru, 2010. "A variable selection method in principal canonical correlation analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1117-1123, April.
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    Cited by:

    1. Fujikoshi, Yasunori, 2022. "High-dimensional consistencies of KOO methods in multivariate regression model and discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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