Estimation for a partial-linear single-index model

Jane Ling Wang*, Liugen Xue, Lixing ZHU, Yun Sam Chong

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

155 Citations (Scopus)


In this paper, we study the estimation for a partial-linear single-index model. A two-stage estimation procedure is proposed to estimate the link function for the single index and the parameters in the single index, as well as the parameters in the linear component of the model. Asymptotic normality is established for both parametric components. For the index, a constrained estimating equation leads to an asymptotically more efficient estimator than existing estimators in the sense that it is of a smaller limiting variance. The estimator of the nonparametric link function achieves optimal convergence rates, and the structural error variance is obtained. In addition, the results facilitate the construction of confidence regions and hypothesis testing for the unknown parameters. A simulation study is performed and an application to a real dataset is illustrated. The extension to multiple indices is briefly sketched.

Original languageEnglish
Pages (from-to)246-274
Number of pages29
JournalAnnals of Statistics
Issue number1
Publication statusPublished - Feb 2010

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Bandwidth
  • Dimension reduction
  • Kernel smoother
  • Local linear smoothing
  • Two-stage estimation


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