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February 2010 Estimation for a partial-linear single-index model
Jane-Ling Wang, Liugen Xue, Lixing Zhu, Yun Sam Chong
Ann. Statist. 38(1): 246-274 (February 2010). DOI: 10.1214/09-AOS712

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.

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Jane-Ling Wang. Liugen Xue. Lixing Zhu. Yun Sam Chong. "Estimation for a partial-linear single-index model." Ann. Statist. 38 (1) 246 - 274, February 2010. https://doi.org/10.1214/09-AOS712

Information

Published: February 2010
First available in Project Euclid: 31 December 2009

zbMATH: 1181.62038
MathSciNet: MR2589322
Digital Object Identifier: 10.1214/09-AOS712

Subjects:
Primary: 62G05
Secondary: 62G20

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

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 1 • February 2010
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