Robust pairwise multiple comparisons under short-tailed symmetric distributions

Date

2015-11-02

Author

Balci, Sibel
Akkaya, Ayşen

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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.

Subject Keywords

62K99, 62F35, 62F10, 62F03, Hypothesis testing, Modified maximum likelihood, Robust estimators, Short-tailed symmetric distribution, Pairwise multiple comparisons

URI

https://hdl.handle.net/11511/41796

Journal

JOURNAL OF APPLIED STATISTICS

DOI

https://doi.org/10.1080/02664763.2015.1023706

Collections

Department of Statistics, Article

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Citation Formats

S. Balci and A. Akkaya, “Robust pairwise multiple comparisons under short-tailed symmetric distributions,” JOURNAL OF APPLIED STATISTICS, pp. 2293–2306, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/41796.