Open Access
May 2018 Efficient estimation for generalized partially linear single-index models
Li Wang, Guanqun Cao
Bernoulli 24(2): 1101-1127 (May 2018). DOI: 10.3150/16-BEJ873


In this paper, we study the estimation for generalized partially linear single-index models, where the systematic component in the model has a flexible semi-parametric form with a general link function. We propose an efficient and practical approach to estimate the single-index link function, single-index coefficients as well as the coefficients in the linear component of the model. The estimation procedure is developed by applying quasi-likelihood and polynomial spline smoothing. We derive large sample properties of the estimators and show the convergence rate of each component of the model. Asymptotic normality and semiparametric efficiency are established for the coefficients in both the single-index and linear components. By making use of spline basis approximation and Fisher score iteration, our approach has numerical advantages in terms of computing efficiency and stability in practice. Both simulated and real data examples are used to illustrate our proposed methodology.


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Li Wang. Guanqun Cao. "Efficient estimation for generalized partially linear single-index models." Bernoulli 24 (2) 1101 - 1127, May 2018.


Received: 1 July 2015; Revised: 1 February 2016; Published: May 2018
First available in Project Euclid: 21 September 2017

zbMATH: 06778360
MathSciNet: MR3706789
Digital Object Identifier: 10.3150/16-BEJ873

Keywords: asymptotic normality , generalized linear model , polynomial splines , quasi-likelihood , semi-parametric regression , Single-index model

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 2 • May 2018
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