Open Access
December 2009 Local quasi-likelihood with a parametric guide
Jianqing Fan, Yichao Wu, Yang Feng
Ann. Statist. 37(6B): 4153-4183 (December 2009). DOI: 10.1214/09-AOS713


Generalized linear models and the quasi-likelihood method extend the ordinary regression models to accommodate more general conditional distributions of the response. Nonparametric methods need no explicit parametric specification, and the resulting model is completely determined by the data themselves. However, nonparametric estimation schemes generally have a slower convergence rate such as the local polynomial smoothing estimation of nonparametric generalized linear models studied in Fan, Heckman and Wand [J. Amer. Statist. Assoc. 90 (1995) 141–150]. In this work, we propose a unified family of parametrically-guided nonparametric estimation schemes. This combines the merits of both parametric and nonparametric approaches and enables us to incorporate prior knowledge. Asymptotic results and numerical simulations demonstrate the improvement of our new estimation schemes over the original nonparametric counterpart.


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Jianqing Fan. Yichao Wu. Yang Feng. "Local quasi-likelihood with a parametric guide." Ann. Statist. 37 (6B) 4153 - 4183, December 2009.


Published: December 2009
First available in Project Euclid: 23 October 2009

zbMATH: 1191.62071
MathSciNet: MR2572456
Digital Object Identifier: 10.1214/09-AOS713

Primary: 62G08
Secondary: 62G20

Keywords: generalized linear model , local polynomial smoothing , parametric guide , quasi-likelihood method

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 6B • December 2009
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