PROFILED FORWARD REGRESSION FOR ULTRAHIGH DIMENSIONAL VARIABLE SCREENING IN SEMIPARAMETRIC PARTIALLY LINEAR MODELS

被引：14

作者：

Liang, Hua ^{[1
]}

Wang, Hansheng ^{[2
]}

Tsai, Chih-Ling ^{[3
]}

机构：

[1] Univ Rochester, Dept Biostat & Computat Biol, Rochester, NY 14642 USA

[2] Peking Univ, Guanghua Sch Management, Beijing 100871, Peoples R China

[3] Univ Calif Davis, Grad Sch Management, Davis, CA 95616 USA

来源：

STATISTICA SINICA | 2012年 / 22卷 / 02期

关键词：

Forward regression; partially linear model; profiled forward regression; screening consistency; ultrahigh dimensional predictor; SELECTION; COEFFICIENT; INFERENCES; LIKELIHOOD; LASSO;

D O I：

10.5705/ss.2010.134

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In partially linear model selection, we develop a profiled forward regression (PFR) algorithm for ultrahigh dimensional variable screening. The PFR algorithm effectively combines the ideas of nonparametric profiling and forward regression. This allows us to obtain a uniform bound for the absolute difference between the profiled predictors and their estimators. Based on this finding, we are able to show that the PFR algorithm uncovers all relevant variables within a few fairly short steps. Numerical studies are presented to illustrate the performance of the proposed method.

引用

页码：531 / 554

页数：24

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