This paper proposes a new Vuong test for the statistical comparison of semi/non-parametric models based on a general quasi-likelihood ratio criterion. An important feature of the new test is its uniformly exact asymptotic size in the overlapping nonnested case, as well as in the easier nested and strictly nonnested cases. The uniform size control is achieved without using pretesting, sample-splitting, or simulated critical values. We also show that the test has nontrivial power against all ƴn-local alternatives and against some local alternatives that converge to the null faster than ƴn. Finally, we provide a framework for conducting uniformly valid post Vuong test inference for model parameters. The finite sample performance of the uniform test and that of the post Vuong test inference procedure are illustrated in a mean-regression example by Monte Carlo.
Co-Author Xiaoxia Shi