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High-Dimensional Consistencies of KOO Methods for the Selection of Variables in Multivariate Linear Regression Models with Covariance Structures

Author

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  • Yasunori Fujikoshi

    (Department of Mathematics, Graduate School of Science, Hiroshima University, 1-3-2 Kagamiyama, Hiroshima 739-8626, Japan)

  • Tetsuro Sakurai

    (School of General and Management Studies, Suwa University of Science, 5000-1 Toyohira, Chino 391-0292, Japan)

Abstract

In this paper, we consider the high-dimensional consistencies of KOO methods for selecting response variables in multivariate linear regression with covariance structures. Here, the covariance structures are considered as (1) independent covariance structure with the same variance, (2) independent covariance structure with different variances, and (3) uniform covariance structure. A sufficient condition for model selection consistency is obtained using a KOO method under a high-dimensional asymptotic framework, such that sample size n , the number p of response variables, and the number k of explanatory variables are large, as in p / n → c 1 ∈ ( 0 , 1 ) and k / n → c 2 ∈ [ 0 , 1 ) , where c 1 + c 2 < 1 .

Suggested Citation

  • Yasunori Fujikoshi & Tetsuro Sakurai, 2023. "High-Dimensional Consistencies of KOO Methods for the Selection of Variables in Multivariate Linear Regression Models with Covariance Structures," Mathematics, MDPI, vol. 11(3), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:671-:d:1049692
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    References listed on IDEAS

    as
    1. 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.
    2. Oda, Ryoya & Suzuki, Yuya & Yanagihara, Hirokazu & Fujikoshi, Yasunori, 2020. "A consistent variable selection method in high-dimensional canonical discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    3. Zhao, L. C. & Krishnaiah, P. R. & Bai, Z. D., 1986. "On detection of the number of signals in presence of white noise," Journal of Multivariate Analysis, Elsevier, vol. 20(1), pages 1-25, October.
    4. Fujikoshi, Yasunori, 2022. "High-dimensional consistencies of KOO methods in multivariate regression model and discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    5. Fujikoshi, Yasunori & Sakurai, Tetsuro, 2016. "High-dimensional consistency of rank estimation criteria in multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 199-212.
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