Reconciling Model Selection and Prediction

It is known that there is a dichotomy in the performance of model selectors. Those that are consistent (having the oracle property) do not achieve the asymptotic minimax rate for prediction error. We look at this phenomenon closely, and argue that the set of parameters on which this dichotomy occurs is extreme, even pathological, and should not be considered when evaluating model selectors. We characterize this set, and show that, when such parameters are dismissed from consideration, consistency and asymptotic minimaxity can be attained simultaneously.