Vuong's closeness test

In statistics, the Vuong closeness test is likelihood-ratio-based test for model selection using the Kullback–Leibler information criterion. This statistic makes probabilistic statements about two models. They can be nested, non-nested or overlapping. The statistic tests the null hypothesis that the two models are equally close to the true data generating process, against the alternative that one model is closer. It cannot make any decision whether the 'closer' model is the true model. In statistics, the Vuong closeness test is likelihood-ratio-based test for model selection using the Kullback–Leibler information criterion. This statistic makes probabilistic statements about two models. They can be nested, non-nested or overlapping. The statistic tests the null hypothesis that the two models are equally close to the true data generating process, against the alternative that one model is closer. It cannot make any decision whether the 'closer' model is the true model. With non-nested models and iid exogenous variables, model 1 (2) is preferred with significance level α, if the z statistic