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Inference procedures based on order statistics

Frey, Jesse C
http://rave.ohiolink.edu/etdc/view?acc_num=osu1122565389

Abstract Details

2005, Doctor of Philosophy, Ohio State University, Statistics.
In this dissertation, we develop several new inference procedures that are based on order statistics. Each procedure is motivated by a particular statistical problem. The first problem we consider is that of computing the probability that a fully-specified collection of independent random variables has a particular ordering. We derive an equal conditionals condition under which such probabilities can be computed exactly, and we also derive extrapolation algorithms that allow approximation and computation of such probabilities in more general settings. Romberg integration is one idea that is used. The second problem we address is that of producing optimal distribution-free confidence bands for a cumulative distribution function. We treat this problem both in the case of simple random sampling and in the more general case in which the sample consists of independent order statistics from the distribution of interest. The latter case includes ranked-set sampling. We propose a family of optimality criteria motivated by the idea that good confidence bands are narrow, and we develop theory that makes the identification and computation of optimal bands possible. The Brunn-Minkowski Inequality from the theory of convex bodies plays a key role in this work. The third problem we investigate is that of how best to take advantage of auxiliary information when estimating a population mean. We develop a general procedure, intentionally representative sampling, that is unbiased in the nonparametric sense, yet offers great flexibility for incorporating auxiliary information. The final problem we consider is that of modeling imperfect judgment rankings in ranked-set sampling. We develop a new class of models so large that essentially any judgment rankings model is a limit of models in this class, and we propose an algorithm for selecting one-parameter families from the class.
Haikady Nagaraja (Advisor)
148 p.
Statistics
Order statistics; Ranked-set sampling; Statistical computing; Confidence bands

Recommended Citations

Citations

  • Frey, J. C. (2005). Inference procedures based on order statistics [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1122565389

    APA Style (7th edition)

  • Frey, Jesse. Inference procedures based on order statistics. 2005. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1122565389.

    MLA Style (8th edition)

  • Frey, Jesse. "Inference procedures based on order statistics." Doctoral dissertation, Ohio State University, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=osu1122565389

    Chicago Manual of Style (17th edition)

osu1122565389
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© 2005, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.