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Testing Parametric Distribution Family Assumptions via Differences in Differential Entropy

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  • Ron Mittelhammer
  • George Judge
  • Miguel Henry

Abstract

We introduce a broadly applicable statistical procedure for testing which parametric distribution family generated a random sample of data. The method, termed the Difference in Differential Entropy (DDE) test, provides a unified framework applicable to a wide range of distributional families, with asymptotic validity grounded in established maximum likelihood, bootstrap, and kernel density estimation principles. The test is straightforward to implement, computationally efficient, and requires no tuning parameters or specialized regularity conditions. It compares an MLE-based estimate of differential entropy under the null hypothesis with a nonparametric bootstrapped kernel density estimate, using their divergence as an information-theoretic measure of model fit.

Suggested Citation

  • Ron Mittelhammer & George Judge & Miguel Henry, 2025. "Testing Parametric Distribution Family Assumptions via Differences in Differential Entropy," Papers 2512.11305, arXiv.org.
    • Handle: RePEc:arx:papers:2512.11305
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    References listed on IDEAS

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    1. 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.
    2. Racine, Jeffrey S. & Maasoumi, Esfandiar, 2007. "A versatile and robust metric entropy test of time-reversibility, and other hypotheses," Journal of Econometrics, Elsevier, vol. 138(2), pages 547-567, June.
    3. Harry Joe, 1989. "Estimation of entropy and other functionals of a multivariate density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(4), pages 683-697, December.
    4. Christian Bontemps & Nour Meddahi, 2012. "Testing distributional assumptions: A GMM aproach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 978-1012, September.
    5. P. M. Robinson, 1991. "Consistent Nonparametric Entropy-Based Testing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(3), pages 437-453.
    6. Lee, Lung-Fei, 1983. "A test for distributional assumptions for the stochastic frontier functions," Journal of Econometrics, Elsevier, vol. 22(3), pages 245-267, August.
    7. Agnieszka Wyłomańska & D Robert Iskander & Krzysztof Burnecki, 2020. "Omnibus test for normality based on the Edgeworth expansion," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-36, June.
    8. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496, December.
    9. 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.
    10. Cho, Jin Seo & White, Halbert, 2011. "Generalized runs tests for the IID hypothesis," Journal of Econometrics, Elsevier, vol. 162(2), pages 326-344, June.
    11. Lee, Lung-Fei, 1986. "Specification Test for Poisson Regression Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(3), pages 689-706, October.
    12. 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.
    13. Christensen, Laurits R & Greene, William H, 1976. "Economies of Scale in U.S. Electric Power Generation," Journal of Political Economy, University of Chicago Press, vol. 84(4), pages 655-676, August.
    14. A. Azzalini & A.W. Bowman, 1990. "A Look at Some Data on the Old Faithful Geyser," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 39(3), pages 357-365, November.
    15. Cadirci, Mehmet Siddik & Evans, Dafydd & Leonenko, Nikolai & Makogin, Vitalii, 2022. "Entropy-based test for generalised Gaussian distributions," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    16. Ai, Chunrong & Sun, Li-Hsien & Zhang, Zheng & Zhu, Liping, 2024. "Testing unconditional and conditional independence via mutual information," Journal of Econometrics, Elsevier, vol. 240(2).
    17. Jurgen A. Doornik & Henrik Hansen, 2008. "An Omnibus Test for Univariate and Multivariate Normality," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 927-939, December.
    18. 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.
    19. Yongmiao Hong & Halbert White, 2005. "Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence," Econometrica, Econometric Society, vol. 73(3), pages 837-901, May.
    20. 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.
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