Response shrinkage estimators in binary regression

A shrinkage type estimator is introduced which has favourable properties in binary regression. The proposed response shrinkage estimator 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 easily computed by using common program packages. They exist also in cases where the number of variables is large as compared to the number of observations. Comparison to alternative shrinkage methods like ridge regression and LASSO shows that response shrinkage performs rather well. Moreover, a combination of response shrinkage estimators and Pregibon's resistant fitting procedure is considered. The resulting estimate corrects for the overprediction of the resistant fitting in a very simple way. Estimators are compared in simulation studies and applications.