Department of Mathematics
Penalized least squares for single index models
The single index model is a useful regression model. In this paper, we propose a nonconcave penalized least squares method to estimate both the parameters and the link function of the single index model. Compared to other variable selection and estimation methods, the proposed method can estimate parameters and select variables simultaneously. When the dimension of parameters in the single index model is a fixed constant, under some regularity conditions, we demonstrate that the proposed estimators for parameters have the so-called oracle property, and furthermore we establish the asymptotic normality and develop a sandwich formula to estimate the standard deviations of the proposed estimators. Simulation studies and a real data analysis are presented to illustrate the proposed methods. © 2010 Elsevier B.V.
Local polynomial regression, Nonconcave penalized least squares, SCAD penalty, Single index model, Variable selection
Source Publication Title
Journal of Statistical Planning and Inference
Link to Publisher's Edition
Peng, H., & Huang, T. (2011). Penalized least squares for single index models. Journal of Statistical Planning and Inference, 141 (4), 1362-1379. https://doi.org/10.1016/j.jspi.2010.10.003