  In this entry we review the generalization error for classification and
single-stage decision problems. We distinguish three alternative definitions of
the generalization error which have, at times, been conflated in the statistics
literature and show that these definitions need not be equivalent even
asymptotically. Because the generalization error is a non-smooth functional of
the underlying generative model, standard asymptotic approximations, e.g., the
bootstrap or normal approximations, cannot guarantee correct frequentist
operating characteristics without modification. We provide simple data-adaptive
procedures that can be used to construct asymptotically valid confidence sets
for the generalization error. We conclude the entry with a discussion of
extensions and related problems.
