Sequential profile Lasso for ultra-high-dimensional partially linear models

Yujie Li, Gaorong Li*, Tiejun TONG

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

2 Citations (Scopus)

Abstract

In this paper, we study ultra-high-dimensional partially linear models when the dimension of the linear predictors grows exponentially with the sample size. For the variable screening, we propose a sequential profile Lasso method (SPLasso) and show that it possesses the screening property. SPLasso can also detect all relevant predictors with probability tending to one, no matter whether the ultra-high models involve both parametric and nonparametric parts. To select the best subset among the models generated by SPLasso, we propose an extended Bayesian information criterion (EBIC) for choosing the final model. We also conduct simulation studies and apply a real data example to assess the performance of the proposed method and compare with the existing method.

Original languageEnglish
Pages (from-to)234-245
Number of pages12
JournalStatistical Theory and Related Fields
Volume1
Issue number2
DOIs
Publication statusPublished - 3 Jul 2017

Scopus Subject Areas

  • Statistics and Probability
  • Analysis
  • Applied Mathematics
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics

User-Defined Keywords

  • extended Bayesian information criterion
  • partially linear model
  • screening property
  • Sequential profile Lasso
  • ultra-high-dimensional data

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