The Annals of Statistics

Local quasi-likelihood with a parametric guide

Jianqing Fan, Yichao Wu, and Yang Feng

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Abstract

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.

Article information

Source
Ann. Statist., Volume 37, Number 6B (2009), 4153-4183.

Dates
First available in Project Euclid: 23 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1256303540

Digital Object Identifier
doi:10.1214/09-AOS713

Mathematical Reviews number (MathSciNet)
MR2572456

Zentralblatt MATH identifier
1191.62071

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62G20: Asymptotic properties

Keywords
Generalized linear model local polynomial smoothing parametric guide quasi-likelihood method

Citation

Fan, Jianqing; Wu, Yichao; Feng, Yang. Local quasi-likelihood with a parametric guide. Ann. Statist. 37 (2009), no. 6B, 4153--4183. doi:10.1214/09-AOS713. https://projecteuclid.org/euclid.aos/1256303540


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