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.