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Information-Theoretic Distribution Test with Application to Normality

  • 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.)

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.

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Paper provided by University of Guelph, Department of Economics and Finance in its series Working Papers with number 0604.

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Length: 23 pages
Date of creation: 2006
Date of revision:
Handle: RePEc:gue:guelph:2006-4
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  1. D. Ormoneit & H. White, 1999. "An efficient algorithm to compute maximum entropy densities," Econometric Reviews, Taylor & Francis Journals, vol. 18(2), pages 127-140.
  2. 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.
  3. 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.
  4. Thanasis Stengos & Yiguo Sun, 2005. "The Absolute Health Income Hypothesis Revisited : A Semiparametric Quantile Regression Approach," University of Cyprus Working Papers in Economics 7-2005, University of Cyprus Department of Economics.
  5. BONTEMPS, Christian & MEDDAHI, Nour, 2002. "Testing Normality : A GMM Approach," Cahiers de recherche 2002-14, Universite de Montreal, Departement de sciences economiques.
  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. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  8. Thanasis Stengos & Ximing Wu, 2005. "Partially Adaptive Estimation via Maximum Entropy Densities," University of Cyprus Working Papers in Economics 6-2005, University of Cyprus Department of Economics.
  9. 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.
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