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ASYMPTOTIC DISTRIBUTIONS FOR TWO ESTIMATORS OF THE SINGLE-INDEX MODEL

Published online by Cambridge University Press:  03 November 2006

Yingcun Xia
Yingcun Xia
Affiliation:
National University of Singapore
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Abstract

The single-index model is one of the most popular semiparametric models in applied quantitative sciences. Two new estimation methods have been proposed recently by Hristache, Juditski, and Spokoiny (2001, Annals of Statistics 29, 595–623) and Xia, Tong, Li, and Zhu (2002, Journal of the Royal Statistical Society, Series B 64, 363–410), respectively. However, their asymptotic distributions have not been investigated yet. In this paper, alternative versions for the methods are investigated. Asymptotic distributions of the estimators are derived. Efficiency comparisons between the estimation methods are made.The author is most grateful to Professor O. Linton and Professor W. Härdle for helpful discussions. Valuable comments from two anonymous reviewers have improved the presentation of the paper substantially. The research has been partially supported by NUS research grant R-155-000-048-112, National University of Singapore, Singapore, and the Alexander von Humboldt Foundation, Germany.

Type
Research Article
Information
Econometric Theory , Volume 22 , Issue 6 , December 2006 , pp. 1112 - 1137
Copyright
© 2006 Cambridge University Press

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