统计与大数据研究院讲座预告：Variable Selection via Partial Correlation
中国人民大学课程研修班老师介绍，统计与大数据研究院将于11月3日举办学术讲座：Variable Selection via Partial Correlation。希望广大学生及在职人士积极参与。
题目：Variable Selection via Partial Correlation
Verne M. Willaman Professor of Statistics,
The Pennsylvania State University
Distinguished Professor, The Pennsylvania State University
Associated Editor of Journal of American Statistical Association
Abstract: Partial correlation based variable selection method was proposed for normal linear regression models by Buhlmann et al (2010) as a comparable alternative method to regularization methods for variable selection. This paper addresses two important issues related to partial correkrion based variable selection method: (a) whether this method is sensitive to normality assumption, and (b) whether this method is valid when the dimension of predictor increases in an exponential rate of the sample size. To address issue (a), we systematically study this method for elliptical linear regression models. Our finding indicates that the original proposal may lead to inferior performance when the marginal kurtosis of predictor is not close to that of normal distribution. Our simulation results further confirm this finding. To ensure the superior performance of partial correlation based variable selection procedure, we propose a thresholded partial correlation (TPC) approach to select significant variables in linear regression models. We establish the selection consistency of tlie TPC in the presence of ultrahigh dimensional predictors. Since the TPC procedure includes the original proposal as a special case, our theoretical results address the issue (b) directly. As a by-product, the sure screening property of the first step of TPC w;is obtained. The numerical examples also illustrate that the TPC is competitively comparable to the commonly-used regularization methods for variable selecrion.