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Information-Theoretic Distribution Test with Application to Normality

Author

Listed:
  • Thanasis Stengos

    (University of Guelph, Canada and The Rimini Centre for Economics Analysis, Rimini, Italy)

  • Ximing Wu†

    (Texas A&M University, USA and University of Guelph, Canada)

Abstract

We derive general distribution tests based on the method of Maximum Entropy density. The proposed tests are derived from maximizing the differential 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.

Suggested Citation

  • Thanasis Stengos & Ximing Wu†, 2007. "Information-Theoretic Distribution Test with Application to Normality," Working Paper series 24_07, Rimini Centre for Economic Analysis.
    • Handle: RePEc:rim:rimwps:24_07
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    References listed on IDEAS

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    1. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January.
    2. Zellner, Arnold & Highfield, Richard A., 1988. "Calculation of maximum entropy distributions and approximation of marginalposterior distributions," Journal of Econometrics, Elsevier, vol. 37(2), pages 195-209, February.
    3. Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February.
    4. Yiguo Sun & Thanasis Stengos, 2008. "The absolute health income hypothesis revisited: a semiparametric quantile regression approach," Empirical Economics, Springer, vol. 35(2), pages 395-412, September.
    5. Jushan Bai & Serena Ng, 2005. "Tests for Skewness, Kurtosis, and Normality for Time Series Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 49-60, January.
    6. Wu, Ximing, 2003. "Calculation of maximum entropy densities with application to income distribution," Journal of Econometrics, Elsevier, vol. 115(2), pages 347-354, August.
    7. Smith, Richard J., 2011. "Gel Criteria For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1192-1235, December.
    8. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 1488, Iowa State University, Department of Economics.
    9. Guido W. Imbens & Richard H. Spady & Phillip Johnson, 1998. "Information Theoretic Approaches to Inference in Moment Condition Models," Econometrica, Econometric Society, vol. 66(2), pages 333-358, March.
    10. Yuichi Kitamura, 2006. "Empirical Likelihood Methods in Econometrics: Theory and Practice," Cowles Foundation Discussion Papers 1569, Cowles Foundation for Research in Economics, Yale University.
    11. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    12. D. Ormoneit & H. White, 1999. "An efficient algorithm to compute maximum entropy densities," Econometric Reviews, Taylor & Francis Journals, vol. 18(2), pages 127-140.
    13. Yuichi Kitamura, 2006. "Empirical Likelihood Methods in Econometrics: Theory and Practice," Levine's Bibliography 321307000000000307, UCLA Department of Economics.
    14. Ximing Wu & Thanasis Stengos, 2005. "Partially adaptive estimation via the maximum entropy densities," Econometrics Journal, Royal Economic Society, vol. 8(3), pages 352-366, December.
    15. Engle, Robert F., 1984. "Wald, likelihood ratio, and Lagrange multiplier tests in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 13, pages 775-826, Elsevier.
    16. Dalén, Jörgen, 1987. "Algebraic bounds on standardized sample moments," Statistics & Probability Letters, Elsevier, vol. 5(5), pages 329-331, August.
    17. Richard Smith, 2005. "Local GEL methods for conditional moment restrictions," CeMMAP working papers CWP15/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. 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.
    19. Yuichi Kitamura, 2006. "Empirical Likelihood Methods in Econometrics: Theory and Practice," CIRJE F-Series CIRJE-F-430, CIRJE, Faculty of Economics, University of Tokyo.
    20. Bera, Anil K. & Jarque, Carlos M., 1981. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals : Monte Carlo Evidence," Economics Letters, Elsevier, vol. 7(4), pages 313-318.
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    Cited by:

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    2. Ekrem Kilic, 2005. "A Nonparametric Way of Distribution Testing," Econometrics 0510006, University Library of Munich, Germany.
    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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