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Information-Theoretic Distribution Test with Application to Normality

Author

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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.

Suggested Citation

  • Thanasis Stengos & Ximing Wu, 2010. "Information-Theoretic Distribution Test with Application to Normality," Econometric Reviews, Taylor & Francis Journals, vol. 29(3), pages 307-329.
    • Handle: RePEc:taf:emetrv:v:29:y:2010:i:3:p:307-329
    DOI: 10.1080/07474930903451565
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    4. Ekrem Kilic, 2005. "A Nonparametric Way of Distribution Testing," Econometrics 0510006, University Library of Munich, Germany.
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    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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