High-dimensional consistency of rank estimation criteria in multivariate linear model

JOURNAL OF MULTIVARIATE ANALYSIS

卷:149

Article

Fujikoshi, Yasunori¹  Sakurai, Tetsuro² 

[1] Hiroshima Univ, Grad Sch Sci, Dept Math, 1-3-1 Kagamiyama, Hiroshima 7398626, Japan

[2] Tokyo Univ Sci, Ctr Gen Educ, Suwa 5000-1 Toyohira, Nagano 3910292, Japan

关键词: AIC;    BIC;    C-p;    Consistency property;    Dimensionality;    Discriminant analysis;    High-dimensional framework;    Multivariate regression model;    Multivariate linear model;    Rank;    Ridge-type criterion;    Tuning parameter;   

DOI  :  10.1016/j.jmva.2016.04.005

来源: Elsevier

【 摘 要 】

This paper is concerned with consistency properties of rank estimation criteria in a multivariate linear model, based on the model selection criteria AIC, BIC and C-p. The consistency properties of these criteria are studied under a high-dimensional framework with two different assumptions on the noncentrality matrix such that the number of response variables and the sample size tend to infinity. In general, it is known that under a large-sample asymptotic framework, the criteria based on AIC and C-p are not consistent, but the criterion based on BIC is consistent. However, we note that there are cases that the criteria based on AIC and C-p are consistent, but the criterion based on BIC is not consistent. Such consistency properties are also shown for the generalized criteria with a tuning parameter. Further, the modified criteria with a ridge-type estimator are also examined. Through a Monte Carlo simulation experiment, our results are checked numerically, and the estimation criteria are compared. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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