报告题目: Random Matrix Theory in High-dimensional Model Selection

主 讲 人：胡 江 

单 位：东北师范大学

时 间：11月30日14:30

腾 讯 ID：240 707 811

摘 要: 

Variable selection in multivariate linear regression is essential for the interpretation, subsequent statistical inferences and predictions of the statistical problem at hand. It has a long history of being studied, and many regressor selection criteria have been proposed. Most commonly used criteria include the Akaike information criterion (AIC), Bayesian information criterion (BIC), and Mallow's Cp and their modifications. It is well-known that if the true model is among the candidate models, then BIC is strongly consistent while AIC is not when only the sample size tends to infinity and the numbers of response variables and regressors remain fixed; a setting often described as large-sample. Increasingly, more and more datasets are viewed as high-dimensional in the sense that the number of response variables p, the number of regressors k and the sample size n tend to infinity such that p/n→c ϵ (0,1) and k/n→αϵ[0,1) with α+c<1. A few recent works reported that, under high dimension, the asymptotic properties of AIC, BIC and Cp selection rules in the large-sample setting do not necessarily carry over in the high-dimensional setting. In this paper, we clarify their asymptotic properties and provide necessary and sufficient conditions for which a selection rule is strongly consistent. We do not assume normality in the errors, and we only require finite fourth moment. The main tool employed is random matrix theory techniques. A consequence of this work states that, under certain mild high-dimensional conditions, if the BIC selection rule is strongly consistent then the AIC selection rule is also strongly consistent, but not vice versa. This result is in stark contrast to the large-sample result.

简 介:

胡江，东北师范大学数学与统计学院副教授，博士生导师，2012年博士毕业于东北师范大学，先后在新加坡国立大学、新加坡南洋理工大学、澳门大学、香港科技大学做研究助理或访问学者。研究方向为大维随机矩阵谱理论及高维统计分析。主持国家自然科学基金面上项目1项、青年科学基金项目1项。近年来在Ann. Statist.、IEEE Trans. Inform. Theory、Bernoulli等重要杂志上发表学术论文二十余篇。现任SCI杂志Random Matrices Theory Appl.编委。