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

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  • Ron Mittelhammer

    (School of Economic Sciences, Washington State University, Pullman, WA 99164, USA)

  • George Judge

    (Graduate School, University of California, Berkeley, CA 92093, USA)

  • Miguel Henry

    (Greylock McKinnon Associates, Boston, MA 02116, USA)

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.

Suggested Citation

  • Ron Mittelhammer & George Judge & Miguel Henry, 2022. "An Entropy-Based Approach for Nonparametrically Testing Simple Probability Distribution Hypotheses," Econometrics, MDPI, vol. 10(1), pages 1-19, January.
  • Handle: RePEc:gam:jecnmx:v:10:y:2022:i:1:p:5-:d:724895
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    References listed on IDEAS

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    1. Bera, Anil K. & Galvao, Antonio F. & Wang, Liang & Xiao, Zhijie, 2016. "A New Characterization Of The Normal Distribution And Test For Normality," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1216-1252, October.
    2. Bera, Anil K & Jarque, Carlos M & Lee, Lung-Fei, 1984. "Testing the Normality Assumption in Limited Dependent Variable Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(3), pages 563-578, October.
    3. Lee, Lung-Fei, 1984. "Tests for the Bivariate Normal Distribution in Econometric Models with Selectivity," Econometrica, Econometric Society, vol. 52(4), pages 843-863, July.
    4. Amengual, Dante & Carrasco, Marine & Sentana, Enrique, 2020. "Testing distributional assumptions using a continuum of moments," Journal of Econometrics, Elsevier, vol. 218(2), pages 655-689.
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