Paul Kabaila, Alan H. Welsh, Rheanna Mainzer
Abstract
We consider the model averaged tail area (MATA) confidence interval proposed by Turek and Fletcher, CSDA, 2012, in the simple situation in which we average over two nested linear regression models. We prove that the MATA for any reasonable weight function belongs to the class of confidence intervals defined by Kabaila and Giri, JSPI, 2009. Each confidence interval in this class is specified by two functions b and s. Kabaila and Giri show how to compute these functions so as to optimize these intervals in terms of satisfying the coverage constraint and minimizing the expected length for the simpler model, while ensuring that the expected length has desirable properties for the full model. These Kabaila and Giri "optimized" intervals provide an upper bound on the performance of the MATA for an arbitrary weight function. This fact is used to evaluate the MATA for a broad class of weights based on exponentiating a criterion related to Mallows' C_P. Our results show that, while far from ideal, this MATA performs surprisingly well, provided that we choose a member of this class that does not put too much weight on the simpler model.