Penalized Likelihood-type Estimators for Generalized Nonparametric Regression

We consider the asymptotic analysis of penalized likelihood type estimators for generalized non-parametric regression problems in which the target parameter is a vector valued function defined in terms of the conditional distribution of a response given a set of covariates. A variety of examples including ones related to generalized linear models and robust smoothing are covered by the theory. Linear approximations to the estimator are constructed using Taylor expansions in Hilbert spaces. An application which is treated is upper bounds on rates of convergence for the penalized likelihood-type estimators. AMS 1980 subject classifications. Primary, 62-G05, Secondary, 62J05, 41-A35, 41-A25, 47-A53, 45-L10, 45-M05.