Institut für Statistik (TUG)
Biometrische Sektion Steiermark-Kärnten - BSSK

We give a large-sample limit analysis of the minimal coverage probability of confidence intervals for location parameters that are constructed based on the outcome of a “conservative” (or “over-consistent”) model selection procedure. We derive an upper bound for the large-sample limit minimal coverage probability of confidence intervals constructed after model selection that applies to a large class of model selection procedures including AIC as well as various general-to-specific and specific-to-general pre-testing procedures.
To our knowledge, this is the first analytical result on the large-sample limit minimal coverage probability of confidence sets constructed after model selection by AIC. This upper bound can be used as a monitor to identify situations where the actual coverage probability can be far below the nominal level.

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Univ.-Prof. DI Dr. Ernst Stadlober