Penalized least squares for single index models

Heng Peng*, Tao Huang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

79 Citations (Scopus)
9 Downloads (Pure)


The single index model is a useful regression model. In this paper, we propose a nonconcave penalized least squares method to estimate both the parameters and the link function of the single index model. Compared to other variable selection and estimation methods, the proposed method can estimate parameters and select variables simultaneously. When the dimension of parameters in the single index model is a fixed constant, under some regularity conditions, we demonstrate that the proposed estimators for parameters have the so-called oracle property, and furthermore we establish the asymptotic normality and develop a sandwich formula to estimate the standard deviations of the proposed estimators. Simulation studies and a real data analysis are presented to illustrate the proposed methods.

Original languageEnglish
Pages (from-to)1362-1379
Number of pages18
JournalJournal of Statistical Planning and Inference
Issue number4
Publication statusPublished - Apr 2011

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

User-Defined Keywords

  • Local polynomial regression
  • Nonconcave penalized least squares
  • SCAD penalty
  • Single index model
  • Variable selection


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