  We consider the problem of estimating the conditional distribution of a
post-model-selection estimator where the conditioning is on the selected model.
The notion of a post-model-selection estimator here refers to the combined
procedure resulting from first selecting a model (e.g., by a model selection
criterion such as AIC or by a hypothesis testing procedure) and then estimating
the parameters in the selected model (e.g., by least-squares or maximum
likelihood), all based on the same data set. We show that it is impossible to
estimate this distribution with reasonable accuracy even asymptotically. In
particular, we show that no estimator for this distribution can be uniformly
consistent (not even locally). This follows as a corollary to (local) minimax
lower bounds on the performance of estimators for this distribution. Similar
impossibility results are also obtained for the conditional distribution of
linear functions (e.g., predictors) of the post-model-selection estimator.
