  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.
