ASYMPTOTIC DISTRIBUTIONS FOR TWO ESTIMATORS OF THE SINGLE-INDEX MODEL

Yingcun Xia

Econometric Theory, 2006, vol. 22, issue 06, pages 1112-1137

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. H rdle 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.

Date: 2006

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