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Variable selection method based on BIC with consistency for non-zero partial correlations under a large-dimensional setting

Author

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  • Takayuki Yamada

    (Kyoto Women’s University)

  • Tetsuro Sakurai

    (Suwa University of Science)

  • Yasunori Fujikoshi

    (Hiroshima University)

Abstract

This paper addresses the problem of selecting non-zero partial correlations under the assumption of normality. It is cumbersome to compute variable selection criteria for all subsets of variable pairs when the number of variables is large, even if it is smaller than the sample size. To tackle this problem, we propose a fast and consistent variable selection method based on Bayesian information criterion (BIC). The consistency of the method is provided in a high-dimensional asymptotic framework such that the sample size and the number of variables both tend toward infinity under a certain rule. Through numerical simulations, it is shown that the proposed method has a high probability of selecting the true subset of pairs of non-zero partial correlation.

Suggested Citation

  • Takayuki Yamada & Tetsuro Sakurai & Yasunori Fujikoshi, 2025. "Variable selection method based on BIC with consistency for non-zero partial correlations under a large-dimensional setting," Computational Statistics, Springer, vol. 40(7), pages 3585-3611, September.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:7:d:10.1007_s00180-025-01628-z
    DOI: 10.1007/s00180-025-01628-z
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    References listed on IDEAS

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    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    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).
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