JSM 2004 - Toronto

Abstract #300044

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Activity Number: 175
Type: Invited
Date/Time: Tuesday, August 10, 2004 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Computing
Abstract - #300044
Title: The Large-sample Minimal-coverage Probability of Confidence Intervals in Regression after Model Selection
Author(s): Hannes Leeb*+ and Paul Kabaila
Companies: Yale University and La Trobe University
Address: 24 Hillhouse Ave., New Haven, CT, 06511,
Keywords: model selection ; confidence intervals ; minimal coverage probability ; AIC ; pre-testing
Abstract:

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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