  In machine learning, the selection of a promising model from a potentially
large number of competing models and the assessment of its generalization
performance are critical tasks that need careful consideration. Typically,
model selection and evaluation are strictly separated endeavors, splitting the
sample at hand into a training, validation, and evaluation set, and only
compute a single confidence interval for the prediction performance of the
final selected model. We however propose an algorithm how to compute valid
lower confidence bounds for multiple models that have been selected based on
their prediction performances in the evaluation set by interpreting the
selection problem as a simultaneous inference problem. We use bootstrap tilting
and a maxT-type multiplicity correction. The approach is universally applicable
for any combination of prediction models, any model selection strategy, and any
prediction performance measure that accepts weights. We conducted various
simulation experiments which show that our proposed approach yields lower
confidence bounds that are at least comparably good as bounds from standard
approaches, and that reliably reach the nominal coverage probability. In
addition, especially when sample size is small, our proposed approach yields
better performing prediction models than the default selection of only one
model for evaluation does.
