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Omnibus Tests for Multivariate Normality of Observations and Residuals

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  • Urzúa, Carlos M.

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.

Suggested Citation

  • Urzúa, Carlos M., 1996. "Omnibus Tests for Multivariate Normality of Observations and Residuals," EGAP Working Papers 200304, Tecnológico de Monterrey, Campus Ciudad de México.
    • Handle: RePEc:ega:docume:200304
    as

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    File URL: http://alejandria.ccm.itesm.mx/egap/documentos/EGAP-2003-04.pdf
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    References listed on IDEAS

    as
    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.
    2. 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 469-489, May.
    3. Urzúa, Carlos M., 1988. "A Class of Maximum-Entropy Multivariate Distributions," EGAP Working Papers 200301, Tecnológico de Monterrey, Campus Ciudad de México.
    4. 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.
    5. 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.
    6. Jarque, C.M. & McKenzie, C.R., 1995. "Testing for multivariate normality in simultaneous equations models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 39(3), pages 323-328.
    7. Urzua, Carlos M., 1996. "On the correct use of omnibus tests for normality," Economics Letters, Elsevier, vol. 53(3), pages 247-251, December.
    8. Bera, A. & John, S., 1983. "Tests for multivariate normality with Pearson alternatives," LIDAM Reprints CORE 534, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    test; multivariate normality; maximum entropy;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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