The Large-Sample Minimal Coverage Probability of Confidence Intervals In Regression After Model Selection

Hannes LeebYale UniversityABSTRACT

This paper contains 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.This upper bound can be used as a monitor to identify situations where the actual coverage probability can be far below the nominal level. We also give an exhaustive characterization of the large-sample limit minimal coverage probability of confidence intervals that are constructed after a preliminary test.

Joint work with Paul Kabaila (La Trobe University)