Date of Award

6-26-2026

Date Published

August 2026

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Advisor(s)

Pinyuen Chen

Second Advisor

Lael Schooler

Keywords

Adaptive elimination;Binomial populations;Curtailed sampling;Ranking and selection;Sequential procedures;Subset selection

Abstract

This dissertation studies sequential subset selection from binomial populations under a frequentist framework. Building on the classical subset selection framework of Gupta and Sobel and later sequential developments, it develops a sequence of refinements designed to improve subset selection efficiency while preserving the required probability of correct selection. The first contribution is a curtailed subset selection procedure that allows sampling to stop once the current leader can no longer be overtaken. The second contribution is a randomized calibration that reduces conservatism caused by the discreteness of the selection threshold and improves the balance between selection accuracy and efficiency. The third contribution is an adaptive elimination refinement that removes populations whose remaining sampling potential is insufficient to reach the current selection boundary. For analytically tractable cases, exact results are derived for the probability of correct selection, the expected sample size, and the expected subset size. For more general settings, conservative approximations and simulation studies are used to examine elimination-induced error and the broader operating characteristics of the proposed procedures. The results show that these refinements preserve the intended selection accuracy while improving sampling efficiency and reducing unnecessary sampling of inferior populations. Taken together, the dissertation shows that classical binomial subset selection admits sequential refinements that remain probabilistically controlled while improving practical efficiency in resource-constrained experiments.

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Open Access

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