Discrepancy Risk Model Selection Test theory for comparing possibly misspecified or nonnested models

Abstract

A new model selection statistical test is proposed for testing the null hypothesis that two probability models equally effectively fit the underlying data generating process (DGP). The new model selection test, called the Discrepancy Risk Model Selection Test (DRMST), extends previous work (see Vuong, 1989) on this problem in four distinct ways. First, generalized goodness-of-fit measures (which include log-likelihood functions) can be used. Second, unlike the classical likelihood ratio test, the models are not required to be fully nested where the nesting concept is defined for generalized goodness-of-fit measures. The DRMST also differs from the likelihood ratio test by not requiring that either competing model provides a completely accurate representation of the DGP. And, fourth, the DRMST may be used to compare competing time-series models using correlated observations as well as data consisting of independent and identically distributed observations.