A robust and efficient estimation method for single index models

JOURNAL OF MULTIVARIATE ANALYSIS

卷:122

Article

Liu, Jicai¹  Zhang, Riquan^1,2  Zhao, Weihua^1,3  Lv, Yazhao¹ 

[1] E China Normal Univ, Sch Finance & Stat, Shanghai 200241, Peoples R China

[2] Shanxi Datong Univ, Dept Math, Datong 037009, Peoples R China

[3] Nantong Univ, Sch Sci, Nantong 226007, Peoples R China

关键词: Single index models;    Modal regression;    Local linear regression;    Robust estimation;    Semiparametric regression;   

DOI  :  10.1016/j.jmva.2013.08.007

来源: Elsevier

【 摘 要 】

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 squares or likelihood are sensitive when there are outliers or the error distribution is heavy tailed. Although an M-type regression is often considered as a good alternative to those methods, it may lose efficiency for normal errors. 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 is established. We show that the proposed estimators are as asymptotically efficient as the least-square-based estimators when there are no outliers and the error distribution is normal. A modified EM algorithm is presented for efficient implementation. The simulations and real data analysis are conducted to illustrate the finite sample performance of the proposed method. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free