A weighted model confidence set: applications to local and mixture model confidence sets

Abstract

Using the Kullback-Leibler (KL) divergence along with Vuong's test, this article constructs a set of appropriate weighted models, say weighted model confidence set, for unknown true density h(·) which is a subset of a class of non-nested models. A weighted confidence set provides an appropriate model for random variable X which some part of its support conveys some important information about the underlying true model. Application of such a weighted model confidence set for local and mixture model confidence sets have been given. Two simulation studies have been conducted to show practical application of our findings.