The Annals of Statistics

Estimation for a partial-linear single-index model

Jane-Ling Wang, Liugen Xue, Lixing Zhu, and Yun Sam Chong

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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.

Article information

Ann. Statist., Volume 38, Number 1 (2010), 246-274.

First available in Project Euclid: 31 December 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation
Secondary: 62G20: Asymptotic properties

Dimension reduction local linear smoothing bandwidth two-stage estimation kernel smoother


Wang, Jane-Ling; Xue, Liugen; Zhu, Lixing; Chong, Yun Sam. Estimation for a partial-linear single-index model. Ann. Statist. 38 (2010), no. 1, 246--274. doi:10.1214/09-AOS712.

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