Simultaneous Inference for Model Averaging of Derived Parameters

Abstract

Model averaging is a useful approach for capturing uncertainty due to model selection. Currently, this uncertainty is often quantified by means of approximations that do not easily extend to simultaneous inference. Moreover, in practice there is a need for both model averaging and simultaneous inference for derived parameters calculated in an after-fitting step. We propose a method for obtaining asymptotically correct standard errors for one or several model-averaged estimates of derived parameters and for obtaining simultaneous confidence intervals that asymptotically control the family-wise Type I error rate. The performance of the method in terms of coverage is evaluated using a simulation study and the applicability of the method is demonstrated by means of three concrete examples.