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Exploring Consistencies of Information Criterion and Test-Based Criterion for High-Dimensional Multivariate Regression Models Under Three Covariance Structures

In: Recent Developments in Multivariate and Random Matrix Analysis

Author

Listed:
  • Tetsuro Sakurai

    (Suwa University of Science, School of General and Management Studies)

  • Yasunori Fujikoshi

    (Hiroshima University, Department of Mathematics, Graduate School of Science)

Abstract

In this paper, we consider the high-dimensional consistency properties of an information criterion and a test-based criterion (KOO method) for the selection of variables in multivariate regression models with covariance structures. The covariance structures considered are (1) an independent covariance structure, (2) a uniform covariance structure and (3) an autoregressive covariance structure. In our model the sample size is not necessarily larger than the dimensionality (number) of response variables. Sufficient conditions for these criteria to be consistent are derived under a high-dimensional asymptotic framework such that the sample size and the dimensionality proceed to infinity together, with their ratio converging to a finite nonzero constant. Our results, and tendencies therein, are explored numerically through a Monte Carlo simulation.

Suggested Citation

  • Tetsuro Sakurai & Yasunori Fujikoshi, 2020. "Exploring Consistencies of Information Criterion and Test-Based Criterion for High-Dimensional Multivariate Regression Models Under Three Covariance Structures," Springer Books, in: Thomas Holgersson & Martin Singull (ed.), Recent Developments in Multivariate and Random Matrix Analysis, chapter 0, pages 313-334, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-56773-6_18
    DOI: 10.1007/978-3-030-56773-6_18
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