Robust Vuong Test for High Dimensional Models

Abstract

This paper provides a new method for model determination. Two important issues are addressed in the general semi/nonparametric framework. First, our method does not require the empirical researchers know the structure of the candidate models, and it can be applied regardless of the candidate models are potentially nested, overlapped or nonnested. Second, our method is robust to the bias introduced by the many series terms in the nonparametric sieve estimators, which makes it more accurate in finite samples. The new method is implemented by testing the null hypothesis that two candidate models have the same goodness of fit. Our test statistic is based on a bias corrected quasi likelihood ratio (B-QLR) statistic, where the bias correction is needed to take care of the potential model degeneracy and high-order bias introduced by the many series terms. We show that our B-QLR statistic, after proper normalization, converges in distribution to the standard normal distribution, which makes our method easy to use and hence attractive for empirical implementation. Inference procedures based on various bootstrap methods are also provided. The finite sample performances of our methods are investigated in simulation studies and an empirical example.