  Generalized linear models are flexible tools for the analysis of diverse
datasets, but the classical formulation requires that the parametric component
is correctly specified and the data contain no atypical observations. To
address these shortcomings we introduce and study a family of nonparametric
full rank and lower rank spline estimators that result from the minimization of
a penalized power divergence. The proposed class of estimators is easily
implementable, offers high protection against outlying observations and can be
tuned for arbitrarily high efficiency in the case of clean data. We show that
under weak assumptions these estimators converge at a fast rate and illustrate
their highly competitive performance on a simulation study and two real-data
examples.
