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Robust pairwise multiple comparisons under short-tailed symmetric distributions

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  • Sibel Balci
  • Aysen Dener Akkaya

Abstract

In one-way ANOVA, most of the pairwise multiple comparison procedures depend on normality assumption of errors. In practice, errors have non-normal distributions so frequently. Therefore, it is very important to develop robust estimators of location and the associated variance under non-normality. In this paper, we consider the estimation of one-way ANOVA model parameters to make pairwise multiple comparisons under short-tailed symmetric (STS) distribution. The classical least squares method is neither efficient nor robust and maximum likelihood estimation technique is problematic in this situation. Modified maximum likelihood (MML) estimation technique gives the opportunity to estimate model parameters in closed forms under non-normal distributions. Hence, the use of MML estimators in the test statistic is proposed for pairwise multiple comparisons under STS distribution. The efficiency and power comparisons of the test statistic based on sample mean, trimmed mean, wave and MML estimators are given and the robustness of the test obtained using these estimators under plausible alternatives and inlier model are examined. It is demonstrated that the test statistic based on MML estimators is efficient and robust and the corresponding test is more powerful and having smallest Type I error.

Suggested Citation

  • Sibel Balci & Aysen Dener Akkaya, 2015. "Robust pairwise multiple comparisons under short-tailed symmetric distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(11), pages 2293-2306, November.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:11:p:2293-2306
    DOI: 10.1080/02664763.2015.1023706
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    References listed on IDEAS

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    1. Ren-Fen Lee & Deng-Yuan Huang, 2003. "On some data oriented robust estimation procedures for means," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(6), pages 625-634.
    2. Ayşen Akkaya & Moti Tiku, 2005. "Robust estimation and hypothesis testing under short-tailedness and inliers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 129-150, June.
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