Wang, Li; Cao, Guanqun Efficient estimation for generalized partially linear single-index models. (English) Zbl 1419.62067 Bernoulli 24, No. 2, 1101-1127 (2018). Summary: 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. Cited in 1 ReviewCited in 5 Documents MSC: 62G05 Nonparametric estimation 62G20 Asymptotic properties of nonparametric inference 62J12 Generalized linear models (logistic models) Keywords:asymptotic normality; generalized linear model; polynomial splines; quasi-likelihood; semi-parametric regression; single-index model PDFBibTeX XMLCite \textit{L. Wang} and \textit{G. Cao}, Bernoulli 24, No. 2, 1101--1127 (2018; Zbl 1419.62067) Full Text: DOI Euclid