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In this paper, we introduce a flexible and widely applicable nonparametricentropy-based testing procedure that can be used to assess the validity ofsimple hypotheses about a specific parametric population distribution. Thetesting methodology relies on the characteristic function of the populationprobability distribution being tested and is attractive in that, regardless ofthe null hypothesis being tested, it provides a unified framework forconducting such tests. The testing procedure is also computationally tractableand relatively straightforward to implement. In contrast to some alternativetest statistics, the proposed entropy test is free from user-specified kerneland bandwidth choices, idiosyncratic and complex regularity conditions, and/orchoices of evaluation grids. Several simulation exercises were performed todocument the empirical performance of our proposed test, including a regressionexample that is illustrative of how, in some contexts, the approach can beapplied to composite hypothesis-testing situations via data transformations.Overall, the testing procedure exhibits notable promise, exhibiting appreciableincreasing power as sample size increases for a number of alternativedistributions when contrasted with hypothesized null distributions. Possiblegeneral extensions of the approach to composite hypothesis-testing contexts,and directions for future work are also discussed.

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