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Information-Theoretic Distribution Test with Application to Normality

  • Thanasis Stengos
  • Ximing Wu

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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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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  1. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January.
  2. Guido W Imbens, Phillip Johnson & Richard H Spady, . "Information theoretic approaches to inference in moment condition model," Economics Papers W12., Economics Group, Nuffield College, University of Oxford.
  3. Thanasis Stengos & Yiguo Sun, 2006. "The absolute health income hypothesis revisited: A Semiparametric Quantile Regression Approach," Working Papers 0606, University of Guelph, Department of Economics and Finance.
  4. 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.
  5. D. Ormoneit & H. White, 1999. "An efficient algorithm to compute maximum entropy densities," Econometric Reviews, Taylor & Francis Journals, vol. 18(2), pages 127-140.
  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. 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.
  9. Imbens, G.W. & Johnson, P. & Spady, R.H., 1995. "Information Theoretic Approaches to Inference in Movement Condition Models," Economics Papers 99, Economics Group, Nuffield College, University of Oxford.
  10. 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.
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