Response smoothing estimators in binary regression

A shrinkage type estimator is introduced which has favorable
properties in binary regression. Although binary observations are
never very far away from the underlying probability, in all
interesting cases there is a non-zero distance between observation
and underlying mean. The proposed response smoothing estimate is
based on a smoothed version of the observed responses which is
obtained by shifting the observation slightly towards the mean of
the observations and therefore closer to the underlying
probability. Estimates of this type are very easily computed by
using common program packages and exist also when the number of
predictors is very large. Moreover, they are robust against
outliers. A combination of response smoothing estimators and
Pregibon's resistant fitting procedure corrects for the
overprediciton of the resistant fitting in a very simple way.
Estimators are compared in simulation studies and applications.