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Normality Testing- A New Direction

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  • Islam, Tanweer ul

Abstract

Abstract This paper is concerned with the evaluation of the performance of the normality tests to ensure the validity of the t-statistics used for assessing significance of regressors in a regression model. For this purpose, we have explored 40 distributions to find the most damaging distribution on the t-statistic. Power comparisons are conducted to find the best performing test against these distributions. It is found that Anderson-Darling statistic is the best option among the five normality tests, Jarque-Bera, Shapiro-Francia, D’Agostino & Pearson, Anderson-Darling & Lilliefors.

Suggested Citation

  • Islam, Tanweer ul, 2008. "Normality Testing- A New Direction," MPRA Paper 16452, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:16452
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    File URL: https://mpra.ub.uni-muenchen.de/16452/1/MPRA_paper_16452.pdf
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    References listed on IDEAS

    as
    1. Bartolucci, F. & Scaccia, L., 2005. "The use of mixtures for dealing with non-normal regression errors," Computational Statistics & Data Analysis, Elsevier, vol. 48(4), pages 821-834, April.
    2. Gel, Yulia R. & Miao, Weiwen & Gastwirth, Joseph L., 2007. "Robust directed tests of normality against heavy-tailed alternatives," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2734-2746, February.
    3. Zaman, Asad & Rousseeuw, Peter J. & Orhan, Mehmet, 2001. "Econometric applications of high-breakdown robust regression techniques," Economics Letters, Elsevier, vol. 71(1), pages 1-8, April.
    4. Jean-Marie Dufour & Abdeljelil Farhat & Lucien Gardiol & Lynda Khalaf, 1998. "Simulation-based finite sample normality tests in linear regressions," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages 154-173.
    5. Onder, A. Ozlem & Zaman, Asad, 2005. "Robust tests for normality of errors in regression models," Economics Letters, Elsevier, vol. 86(1), pages 63-68, January.
    6. Bonett, Douglas G. & Seier, Edith, 2002. "A test of normality with high uniform power," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 435-445, September.
    7. Yanagihara, Hirokazu, 2003. "Asymptotic expansion of the null distribution of test statistic for linear hypothesis in nonnormal linear model," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 222-246, February.
    8. Urzua, Carlos M., 1996. "On the correct use of omnibus tests for normality," Economics Letters, Elsevier, vol. 53(3), pages 247-251, December.
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    More about this item

    Keywords

    Normality test; power of the test; t-statistic;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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