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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Abstract

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

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

Dates
First available in Project Euclid: 31 December 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1262271615

Digital Object Identifier
doi:10.1214/09-AOS712

Mathematical Reviews number (MathSciNet)
MR2589322

Zentralblatt MATH identifier
1181.62038

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1262271615


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