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Information-Theoretic Distribution Test with Application to Normality

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  • Thanasis Stengos
  • Ximing Wu

Abstract

We derive general distribution tests based on the method of maximum entropy (ME) density. The proposed tests are derived from maximizing the differential entropy subject to given moment constraints. By exploiting the equivalence between the ME and maximum likelihood (ML) estimates for the general exponential family, we can use the conventional likelihood ratio (LR), Wald, and Lagrange multiplier (LM) testing principles in the maximum entropy framework. In particular, we use the LM approach to derive tests for normality. Monte Carlo evidence suggests that the proposed tests are compatible with and sometimes outperform some commonly used normality tests. We show that the proposed tests can be extended to tests based on regression residuals and non-i.i.d. data in a straightforward manner. An empirical example on production function estimation is presented.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 29 (2010)
Issue (Month): 3 ()
Pages: 307-329

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Handle: RePEc:taf:emetrv:v:29:y:2010:i:3:p:307-329

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Related research

Keywords: Distribution test; Maximum entropy; Normality;

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References

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  1. 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.
  2. 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.
  3. Guido W. Imbens & Phillip Johnson & Richard H. Spady, 1995. "Information Theoretic Approaches to Inference in Moment Condition Models," NBER Technical Working Papers 0186, National Bureau of Economic Research, Inc.
  4. Christian Bontemps & Nour Meddahi, 2002. "Testing Normality: A GMM Approach," CIRANO Working Papers 2002s-63, CIRANO.
  5. 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.
  6. 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.
  7. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  8. D. Ormoneit & H. White, 1999. "An efficient algorithm to compute maximum entropy densities," Econometric Reviews, Taylor & Francis Journals, vol. 18(2), pages 127-140.
  9. Wu, Ximing, 2003. "Calculation of maximum entropy densities with application to income distribution," Journal of Econometrics, Elsevier, vol. 115(2), pages 347-354, August.
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Cited by:
  1. 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.
  2. Tack, Jesse, 2013. "A Nested Test for Common Yield Distributions with Applications to U.S. Corn," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 38(1), April.
  3. Ekrem Kilic, 2005. "A Nonparametric Way of Distribution Testing," Econometrics 0510006, EconWPA.
  4. Hend Auda, 2013. "Novel symmetry tests in regression models based on Gini mean difference," METRON, Springer, vol. 71(1), pages 21-32, June.

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