Profile forward regression screening for ultra-high dimensional semiparametric varying coefficient partially linear models

JOURNAL OF MULTIVARIATE ANALYSIS

卷:155

Article

Li, Yujie¹  Li, Gaorong²  Lian, Heng³  Tong, Tiejun⁴ 

[1] Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China

[2] Beijing Univ Technol, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China

[3] City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

[4] Hong Kong Baptist Univ, Dept Math, Hong Kong, Hong Kong, Peoples R China

关键词: Varying coefficient partially linear model;    Profile forward regression;    Variable screening;    Screening consistency property;    Ultra-high dimension;    EBIC;   

DOI  :  10.1016/j.jmva.2016.12.006

来源: Elsevier

【 摘 要 】

In this paper, we consider semiparametric varying coefficient partially linear models when the predictor variables of the linear part are ultra-high dimensional where the dimensionality grows exponentially with the sample size. We propose a profile forward regression (PFR) method to perform variable screening for ultra-high dimensional linear predictor variables. The proposed PFR algorithm can not only identify all relevant predictors consistently even for ultra-high semiparametric models including both nonparametric and parametric parts, but also possesses the screening consistency property. To determine whether or not to include the candidate predictor in the model of selected ones, we adopt an extended Bayesian information criterion (EBIC) to select the best candidate model. Simulation studies and a real data example are also carried out to assess the performance of the proposed method and to compare it with existing screening methods. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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