A Robust And Efficient Estimation Method for Single Index Models

Zhang Riquan; Liu Jicai; Zhao Weihua; Lv Yazhao

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A Robust And Efficient Estimation Method for Single Index Models

Zhang Riquan 1 * #,Liu Jicai 2,Zhao Weihua 2,Lv Yazhao 2

1.School of Finance and Statistics, East China Normal University, ShangHai 200240

2.School of Finance and Statistics, East China Normal University

*Correspondence author

#Submitted by

Subject:

Funding: National Natural Science Foundation of China （No.No. 11171112）, Doctoral Fund of Ministry of Education of China （No.No. 20090076110001）, National Statistical Science Research Major Program of China （No.No. 2001LZ051）

Opened online:18 January 2013

Accepted by: none

Citation: Zhang Riquan,Liu Jicai,Zhao Weihua.A Robust And Efficient Estimation Method for Single Index Models[OL]. [18 January 2013] http://en.paper.edu.cn/en_releasepaper/content/4502718

Single index models are natural extensions of linear models and overcome the so-called curse of dimensionality. They have applications to many fields, such as medicine, economics and finance. However, most existing methods based on least square or likelihood, are sensitive to outliers and lose efficiency for heavy-tail error distribution. In this paper, we propose a new robust and efficient estimation procedure based on local modal regression for single index models. The asymptotic normality of proposed estimators for both the parametric and nonparametric parts are established. We propose a modified EM algorithm for the proposed estimation procedure. The simulations and real data analysis are conducted to illustrate the finite sample performance of the proposed method.

Keywords:Single index models; modal regression; local linear regression; robust estimation; semiparametric regression

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