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New Graphical Methods and Test Statistics for Testing Composite Normality

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  • Marc S. Paolella

    (Department of Banking and Finance, University of Zurich, Plattenstrasse 14, 8032 Zurich, Switzerland
    Swiss Finance Institute, Walchestrasse 9 CH-8006 Zurich, Switzerland)

Abstract

Several graphical methods for testing univariate composite normality from an i.i.d. sample are presented. They are endowed with correct simultaneous error bounds and yield size-correct tests. As all are based on the empirical CDF, they are also consistent for all alternatives. For one test, called the modified stabilized probability test, or MSP, a highly simplified computational method is derived, which delivers the test statistic and also a highly accurate p-value approximation, essentially instantaneously. The MSP test is demonstrated to have higher power against asymmetric alternatives than the well-known and powerful Jarque-Bera test. A further size-correct test, based on combining two test statistics, is shown to have yet higher power. The methodology employed is fully general and can be applied to any i.i.d. univariate continuous distribution setting.

Suggested Citation

  • Marc S. Paolella, 2015. "New Graphical Methods and Test Statistics for Testing Composite Normality," Econometrics, MDPI, vol. 3(3), pages 1-29, July.
    • Handle: RePEc:gam:jecnmx:v:3:y:2015:i:3:p:532-560:d:52631
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    References listed on IDEAS

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    1. Sivan Aldor-Noiman & Lawrence D. Brown & Andreas Buja & Wolfgang Rolke & Robert A. Stine, 2014. "Aldor-Noiman, S., Brown, L.D., Buja, A., Rolke, W., and Stine, R.A. (2013), "The Power to See: A New Graphical Test of Normality," The American Statistician , 67, 249-260," The American Statistician, Taylor & Francis Journals, vol. 68(4), pages 318-318, November.
    2. Thanasis Stengos & Ximing Wu, 2010. "Information-Theoretic Distribution Test with Application to Normality," Econometric Reviews, Taylor & Francis Journals, vol. 29(3), pages 307-329.
    3. Einmahl, J.H.J. & McKeague, I.W., 1999. "Confidence tubes for multiple quantile plots via empirical likelihood," Other publications TiSEM b64493f8-1c01-40fd-b16d-7, Tilburg University, School of Economics and Management.
    4. 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.
    5. Sivan Aldor-Noiman & Lawrence D. Brown & Andreas Buja & Wolfgang Rolke & Robert A. Stine, 2013. "The Power to See: A New Graphical Test of Normality," The American Statistician, Taylor & Francis Journals, vol. 67(4), pages 249-260, November.
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    Cited by:

    1. Gambacciani, Marco & Paolella, Marc S., 2017. "Robust normal mixtures for financial portfolio allocation," Econometrics and Statistics, Elsevier, vol. 3(C), pages 91-111.
    2. Marc S. Paolella, 2017. "The Univariate Collapsing Method for Portfolio Optimization," Econometrics, MDPI, vol. 5(2), pages 1-33, May.
    3. Paolella, Marc S., 2017. "Asymmetric stable Paretian distribution testing," Econometrics and Statistics, Elsevier, vol. 1(C), pages 19-39.

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