Testing Several Rival Models Using the Extension of Vuong's Test and Quasi Clustering

The two main goals in model selection are firstly introducing an approach to test homogeneity of several rival models and secondly selecting a set of reasonable models or estimating the best rival model to the true one. In this paper we extend Vuong's method for several models to cluster them. Based on the working paper of Katayama $(2008)$, we propose an approach to test whether rival models have expected relations. The multivariate extension of Vuong's test gives the opportunity to examine some hypotheses about the rival models and their relations with respect to the unknown true model. On the other hand, the standard method of model selection provides an implementation of Occam's razor, in which parsimony or simplicity is balanced against goodness of fit. Therefore, we are interested in clustering the rival models based on their divergence from the true model to select a suitable set of rival models. In this paper we have introduced two approaches to select suitable sets of rival models based on the multivariate extension of Vuong's test and quasi clustering approach.