Department of Mathematics
Estimation for a partial-linear single-index model
In this paper, we study the estimation for a partial-linear single-index model. A two-stage estimation procedure is proposed to estimate the link function for the single index and the parameters in the single index, as well as the parameters in the linear component of the model. Asymptotic normality is established for both parametric components. For the index, a constrained estimating equation leads to an asymptotically more efficient estimator than existing estimators in the sense that it is of a smaller limiting variance. The estimator of the nonparametric link function achieves optimal convergence rates, and the structural error variance is obtained. In addition, the results facilitate the construction of confidence regions and hypothesis testing for the unknown parameters. A simulation study is performed and an application to a real dataset is illustrated. The extension to multiple indices is briefly sketched. © 2010. Institute of Mathematical Statistics.
Bandwidth, Dimension reduction, Kernel smoother, Local linear smoothing, Two-stage estimation
Source Publication Title
Annals of Statistics
Institute of Mathematical Statistics
Wang, Jane-Ling, Liugen Xue, Lixing Zhu, and Yun Sam Chong. "Estimation for a partial-linear single-index model." Annals of Statistics 38.1 (2009): 246-274.