  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.
