Rich model classes needed by modern applications may be too complex to admit uniformly consistent estimators. However, these rich classes may still allow for estimators with pointwise guarantees whose performance can be bounded in a model-dependent way. But the drawback of the pointwise angle is that estimator performance a function of the very unknown model that is being estimated. Therefore, how well a consistent estimator is doing may not be clear no matter what the sample size. 

Departing from this uniform/pointwise dichotomy, we examine a new framework for rich model classes admitting only pointwise consistency, but all information needed to gauge estimator performance can be obtained from the data. We examine universal compression and prediction in this setting.