DOI

10.17077/etd.p6j5lhlv

Document Type

Dissertation

Date of Degree

Spring 2018

Degree Name

PhD (Doctor of Philosophy)

Degree In

Biostatistics

First Advisor

Cavanaugh, Joseph

Second Advisor

Neath, Andrew

First Committee Member

Polgreen, Linnea

Second Committee Member

Polgreen, Philip

Third Committee Member

Oleson, Jacob

Fourth Committee Member

Foster, Eric

Abstract

Discrepancy measures are often employed in problems involving the selection and assessment of statistical models. A discrepancy gauges the separation between a fitted candidate model and the underlying generating model. In this work, we consider pairwise comparisons of fitted models based on a probabilistic evaluation of the ordering of the constituent discrepancies. An estimator of the probability is derived using the bootstrap.

In the framework of hypothesis testing, nested models are often compared on the basis of the p-value. Specifically, the simpler null model is favored unless the p-value is sufficiently small, in which case the null model is rejected and the more general alternative model is retained. Using suitably defined discrepancy measures, we mathematically show that, in general settings, the Wald, likelihood ratio (LR) and score test p-values are approximated by the bootstrapped discrepancy comparison probability (BDCP). We argue that the connection between the p-value and the BDCP leads to potentially new insights regarding the utility and limitations of the p-value. The BDCP framework also facilitates discrepancy-based inferences in settings beyond the limited confines of nested model hypothesis testing.

Keywords

bootstrap, discrepancy functions, hypothesis testing, model evaluation, model selection, p-value

Pages

xvii, 117 pages

Bibliography

Includes bibliographical references (pages 112-117).

Copyright

Copyright © 2018 Benjamin N. Riedle

Included in

Biostatistics Commons

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