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Computer Age Statistical Inference by Trevor Hastie, Bradley Efron

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20 Inference After Model Selection

The classical theory of model selection focused on “F tests” performed within Gaussian regression models. Inference after model selection (for instance, assessing the accuracy of a fitted regression curve) was typically done ignoring the model selection process. This was a matter of necessity: the combination of discrete model selection and continuous regression analysis was too awkward for simple mathematical description. Electronic computation has opened the door to a more honest analysis of estimation accuracy, one that takes account of the variability induced by data-based model selection.

Figure 20.1 displays the cholesterol data, an example we will use for illustration in what follows: cholestyramine, ...

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