Author

Jeremy Entner

Date of Award

8-2013

Degree Type

Dissertation

Embargo Date

2-3-2014

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Advisor(s)

Pinyuen Chen

Keywords

Depth, Multivariate, Nonparametric, Ranking and Selection

Subject Categories

Mathematics

Abstract

In a Ranking and Selection problem, a collection of k populations is given which follow some (partially) unknown probability distributions. The problem is to select the "best" of the k populations where "best" is well defined in terms of some unknown population parameter. In many univariate parametric and nonparamentric settings, solutions to these ranking and selection problems exist. In the multivariate case, only parametric solutions have been developed. We have developed several methods for solving nonparametric multivariate ranking and selection problems. The problems considered allow an experimenter to select the "best" populations based on nonparametric notions of dispersion, location, and distribution. For the first two problems, we use Tukey's Halfspace Depth to define these notions. In the last problem, we make use of a multivariate version of the Kolmogorov-Smirnov Statistic for making selections.

Access

Open Access

Included in

Mathematics Commons

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