Finite sample properties of confidence intervals centered on a model averaged estimator

Abstract

We examine confidence intervals centered on the frequentist model averaged estimator proposed by Buckland et al. (1997). We consider two formulas for the standard error of this estimator: the estimate put forward by Buckland et al. (1997) of their formula (9) and the square root of formula (6.12) of Burnham and Anderson (2002). We also consider four procedures that have been suggested in the literature for obtaining the half-width of the confidence interval from the chosen standard error. We assess the exact finite sample performances of the eight resulting confidence intervals using a simple testbed situation consisting of two nested linear regression models. This is done by deriving exact expressions for the confidence intervals and then for the coverages and scaled expected lengths of these confidence intervals. We also explore the performances of these confidence intervals in the limit as the residual degrees of freedom diverges to infinity.