Date of Award

5-2005

Degree Type

Thesis

Degree Name

M.S.

Degree Program

Mathematics

Department

Mathematics

Major Professor

Solanky, Tumulesh

Second Advisor

Li, Linxiong

Third Advisor

Watkins, Terry

Fourth Advisor

Fang, Zhide

Abstract

In a pioneering work, Bechhofer (1954) introduced the concept of indifference-zone formulation and formulated some methodologies in the case of the problem of selecting the best normal population. In statistical literature, many vector-at-a time and unbalanced methodologies are available for the selecting the best normal population. However, the literature is not that rich for the partition problem. In this thesis, an unbalanced methodology of sampling along the lines of Mukhopadhyay and Solanky (2002) is introduced for the partition problem. A two-stage and a purely sequential procedure are introduced which take c observations from the control population from the control population for each observation from each of the non-control population. The theoretical second-order asymptotics of the two introduced procedures are derived and studied for small to moderate sample sizes via Monte Carlo simulations. The robustness of various already known procedures in the statistical literature and the ones proposed in this thesis are studied via simulation studies. An attempt has also been made to determine the optimal choice of the value of c.

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The University of New Orleans and its agents retain the non-exclusive license to archive and make accessible this dissertation or thesis in whole or in part in all forms of media, now or hereafter known. The author retains all other ownership rights to the copyright of the thesis or dissertation.

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