Estimation and testing for partially linear single-index models
Abstract
In partially linear single-index models, we obtain the semiparametrically efficient profile least-squares estimators of regression coefficients. We also employ the smoothly clipped absolute deviation penalty (SCAD) approach to simultaneously select variables and estimate regression coefficients. We show that the resulting SCAD estimators are consistent and possess the oracle property. Subsequently, we demonstrate that a proposed tuning parameter selector, BIC, identifies the true model consistently. Finally, we develop a linear hypothesis test for the parametric coefficients and a goodness-of-fit test for the nonparametric component, respectively. Monte Carlo studies are also presented.
Cite
@article{arxiv.1211.3509,
title = {Estimation and testing for partially linear single-index models},
author = {Hua Liang and Xiang Liu and Runze Li and Chih-Ling Tsai},
journal= {arXiv preprint arXiv:1211.3509},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/10-AOS835 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)