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Omnibus Tests for Multivariate Normality of Observations and Residuals

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Author Info
Urzúa, Carlos M.

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Abstract

This paper provides omnibus tests for multivariate normality of both observations and residuals. They are derived by considering as the alternatives to the multivariate normal a class of maximum-entropy distributions studied elsewhere by the author. The tests, being Lagrange multiplier statistics, have optimum local asymptotic power among those alternatives. Furthermore, they coincide in the univariate case with the popular Jarque-Bera test for normality. They also include as special cases several multivariate tests available in the literature. Finally, the paper also suggests simple adjustments that can significantly improve the power of the tests in the case of small and medium size samples, even for the univariate case.

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File URL: http://alejandria.ccm.itesm.mx/egap/documentos/EGAP-2003-04.pdf
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Publisher Info
Paper provided by Tecnológico de Monterrey, Campus Ciudad de México in its series EGAP Working Papers with number 200304.

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Date of creation: Dec 1996
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Publication status: Published in Advances in Econometrics, 1997, vol. 12, pp. 341-358.
Handle: RePEc:ega:docume:200304

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Web page: http://www.ccm.itesm.mx/egap/
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Related research
Keywords: test; multivariate normality; maximum entropy;

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing

References listed on IDEAS
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  1. 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. [Downloadable!] (restricted)
  2. Urzúa, Carlos M., 1988. "A Class of Maximum-Entropy Multivariate Distributions," EGAP Working Papers 200301, Tecnológico de Monterrey, Campus Ciudad de México. [Downloadable!]
  3. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259. [Downloadable!] (restricted)
  4. Urzua, Carlos M, 1990. "Lending to Sovereign Borrowers: Snapshots of the Eurocurrency Market Using a Thomian Camera," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(2), pages 469-89, May. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
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