Model Confidence Set Based on Kullback-Leibler Divergence Distance

Consider the problem of estimating true density, h(·) based upon a random sample X1, . . . , Xn. In general, h(·) is approximated using an appropriate (in some sense, see below) model fθ(x). This article using Vuong’s (1989) test along with a collection of k(> 2) non-nested models constructs a set of appropriate models, say model confidence set, for unknown model h(·). Application of such confidence set has been confirmed through a simulation study.