LE3 .A278 2022

2022

Peng, Jianan

Acadia University

Master of Science

Masters

Mathematics and Statistics

Mathematics & Statistics

The majority of work on multiple comparisons is on comparing the means of k ⩾3 populations following the work of Tukey (1953) on pairwise comparisons of k population means, of Dunnett (1955) on comparisons of several means with a control mean, and of Scheff ́e (1953) on all-contrast comparisons among the population means. This thesis focuses on five different methods to construct simultaneous confidence intervals for successive comparisons under heteroscedasticity. Th five methods are the MaxT method and MinP method introduced by Westfall and Young (1993) along with the F1 and F2 methods introduced by Xiong and Mu (2009) and the H method introduced in Hannig et al. (2006). Two types of fiducial generalized pivotal quantities (FGPQ) based confidence intervals by Xiong and Mu (2009) and one FGPQ based confidence interval by Hannig et al. (2006). These five methods were developed for two-sided pairwise comparisons. Weprove that the FGPQ-based successive confidence intervals have asymptotically correct coverage. Simulation studies and numerical examples are presented.

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https://scholar.acadiau.ca/islandora/object/theses:3735