Local quasi-likelihood with a parametric guide

Details Local quasi-likelihood with a parametric guide Local quasi-likelihood with a parametric guide

2009-11-20

arxiv.org/abs/0911.4021v1

Annals of Statistics 2009, Vol. 37, No. 6B, 4153-4183

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/09-AOS713 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

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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