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

Yujie Li, Gaorong Li*, Heng Lian, Tiejun TONG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)133-150
Number of pages18
JournalJournal of Multivariate Analysis
Volume155
DOIs
Publication statusPublished - 1 Mar 2017

Scopus Subject Areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • EBIC
  • Profile forward regression
  • Screening consistency property
  • Ultra-high dimension
  • Variable screening
  • Varying coefficient partially linear model

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