  We introduce and study a family of robust estimators for the functional
logistic regression model whose robustness automatically adapts to the data
thereby leading to estimators with high efficiency in clean data and a high
degree of resistance towards atypical observations. The estimators are based on
the concept of density power divergence between densities and may be formed
with any combination of lower rank approximations and penalties, as the need
arises. For these estimators we prove uniform convergence and high rates of
convergence with respect to the commonly used prediction error under fairly
general assumptions. The highly competitive practical performance of our
proposal is illustrated on a simulation study and a real data example which
includes atypical observations.
