title: 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.
authors.affiliation: Department of Biostatistics and Computational Biology, University of Rochester, Rochester, New York 14642, USA,  hliang@bst.rochester.edu ,  xliu@bst.rochester.edu.
authors.forename: Hua
authors.initials: H
authors.lastname: Liang
authors.forename: Xiang
authors.initials: X
authors.lastname: Liu
authors.forename: Runze
authors.initials: R
authors.lastname: Li
authors.forename: Chih-Ling
authors.initials: CL
authors.lastname: Tsai