Estimation and testing for partially linear single-index models

Hua Liang, Xiang Liu, Runze Li, Chih Ling Tsai

Research output: Contribution to journalArticlepeer-review

152 Scopus citations

Abstract

In partially linear single-index models, we obtain the semiparametrically efficient profile least-squares estimators of regression coefficients. We also employ the smoothly clipped absolute deviation penalty (SCAD) approach to simultaneously select variables and estimate regression coefficients. We show that the resulting SCAD estimators are consistent and possess the oracle property. Subsequently, we demonstrate that a proposed tuning parameter selector, BIC, identifies the true model consistently. Finally, we develop a linear hypothesis test for the parametric coefficients and a goodness-of-fit test for the nonparametric component, respectively. Monte Carlo studies are also presented.

Original languageEnglish (US)
Pages (from-to)3811-3836
Number of pages26
JournalAnnals of Statistics
Volume38
Issue number6
DOIs
StatePublished - Dec 2010

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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