On the minimum coverage probability of model averaged tail area confidence intervals

Abstract

AbstractFrequentist model averaging has been proposed as a method for incorporating “model uncertainty” into confidence interval construction. Such proposals have been of particular interest in the environmental and ecological statistics communities. A promising method of this type is the model averaged tail area (MATA) confidence interval put forward by Turek & Fletcher (2012). The performance of this interval depends greatly on the data‐based model weights. A computationally convenient formula for the coverage probability of this interval was provided by Kabaila, Welsh, & Abeysekera (2016), in the simple scenario of two nested linear regression models. We consider more complicated scenarios with a large number of linear regression models. For each of a given set of components of the regression parameter vector, we either set the component to zero or let it vary freely. We provide an easily computed upper bound on the minimum coverage probability of the MATA confidence interval. This upper bound provides evidence against the use of a model weight based on the Bayesian Information Criterion (BIC). The Canadian Journal of Statistics 46: 279–297; 2018 © 2018 Statistical Society of Canada