An Entropy-Based Approach for Nonparametrically Testing Simple Probability Distribution Hypotheses

Abstract: In this paper, we introduce a flexible and widely applicable nonparametric entropy-based testing procedure that can be used to assess the validity of simple hypotheses about a specific parametric population distribution. The testing methodology relies on the characteristic function of the population probability distribution being tested and is attractive in that, regardless of the null hypothesis being tested, it provides a unified framework for conducting such tests. The testing procedure is also computationally tractable and relatively straightforward to implement. In contrast to some alternative test statistics, the proposed entropy test is free from user-specified kernel and bandwidth choices, idiosyncratic and complex regularity conditions, and/or choices of evaluation grids. Several simulation exercises were performed to document the empirical performance of our proposed test, including a regression example that is illustrative of how, in some contexts, the approach can be applied to composite hypothesis-testing situations via data transformations. Overall, the testing procedure exhibits notable promise, exhibiting appreciable increasing power as sample size increases for a number of alternative distributions when contrasted with hypothesized null distributions. Possible general extensions of the approach to composite hypothesis-testing contexts, and directions for future work are also discussed.