A robust and efficient estimation method for single index models

作者：Liu, Jicai; Zhang, Riquan^*; Zhao, Weihua; Lv, Yazhao

来源：Journal of Multivariate Analysis, 2013, 122: 226-238.

DOI：10.1016/j.jmva.2013.08.007

• Single index models
• Modal regression
• Local linear regression
• Robust estimation
• Semiparametric regression

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.

• 出版日期2013-11
• 单位华东师范大学; 南通大学; 山西大同大学