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Information-Theoretic Distribution Test with Application to Normality

Author

Listed:
  • Thanasis Stengos

    (Department of Economics, University of Guelph.)

  • Ximing Wu

    (Department of Agricultural Economics, Texas A&M University and Department of Economics, University of Guelph.)

Abstract
We derive general distribution tests based on the method of Maximum Entropy density. The proposed tests are derived from maximizing the di®erential entropy subject to moment constraints. By exploiting the equivalence between the Maximum Entropy and Maximum Likelihood estimates of the general exponential family, we can use the conventional Likelihood Ratio, Wald and Lagrange Multiplier testing principles in the maximum entropy framework. In particular, we use the Lagrange Multiplier method to derive tests for normality and their asymptotic properties. Monte Carlo evidence suggests that the proposed tests have desirable small sample properties and often outperform commonly used tests such as the Jarque-Bera test and the Kolmogorov-Smirnov-Lillie test for normality. We show that the proposed tests can be extended totests based on regression residuals and non-iid data in a straightforward manner. We apply the proposed tests to the residuals from a stochastic production frontier model and reject the normality hypothesis.

Suggested Citation

  • Thanasis Stengos & Ximing Wu, 2006. "Information-Theoretic Distribution Test with Application to Normality," Working Papers 0604, University of Guelph, Department of Economics and Finance.
    • Handle: RePEc:gue:guelph:2006-4
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    References listed on IDEAS

    as
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    Cited by:

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    3. Lee Tae-Hwy & Wang He & Xi Zhou & Zhang Ru, 2023. "Density Forecast of Financial Returns Using Decomposition and Maximum Entropy," Journal of Econometric Methods, De Gruyter, vol. 12(1), pages 57-83, January.
    4. Meniago, Christelle & Mukuddem-Petersen, Janine & Petersen, Mark A. & Mongale, Itumeleng P., 2013. "What causes household debt to increase in South Africa?," Economic Modelling, Elsevier, vol. 33(C), pages 482-492.
    5. Hend Auda, 2013. "Novel symmetry tests in regression models based on Gini mean difference," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 21-32, June.
    6. Marc S. Paolella, 2015. "New Graphical Methods and Test Statistics for Testing Composite Normality," Econometrics, MDPI, vol. 3(3), pages 1-29, July.
    7. Fournier, B. & Rupin, N. & Bigerelle, M. & Najjar, D. & Iost, A. & Wilcox, R., 2007. "Estimating the parameters of a generalized lambda distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2813-2835, March.

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    More about this item

    Keywords

    distribution test; maximum entropy; normality.;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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