Degree Type

Thesis

Date of Award

2020

Degree Name

Doctor of Philosophy

Department

Statistics

Major

Statistics

First Advisor

Dan Nettleton

Abstract

This dissertation is made up of three projects, all of which focus on prediction or uncertainty quantification with parametric and nonparametric methods.

Chapter 2 introduces novel approaches to generating semiparametric prediction intervals for linear models. We compare these new methods to other prediction interval methods with simulated and real-world data. We show our method is competitive with other methods in most cases, and better in a subset of cases. We provide multiple theorems related to the marginal coverage of the new methods. We also use these methods to provide estimation for event outcomes in the sports realm. The results show the effectiveness of our methods in providing asymptotically valid, semiparametric prediction intervals.

Chapter 3 introduces a new R package that implements multiple state-of-the-art methodologies to generate prediction intervals for random forests. We compare these methods via simulation. We also apply a subset of these methods to a drug-discovery data analysis problem.

Chapter 4 introduces multiple monotone restriction methods for random forest predictions. We compare our methods to other tree-based monotone restriction methods, showing that our method stays competitive, while guaranteeing partially monotone predictions. We also extend our monotone restriction methods to generate monotone restricted prediction intervals for random forests.

DOI

https://doi.org/10.31274/etd-20210114-72

Copyright Owner

Chancellor Anthony James Johnstone

Language

en

File Format

application/pdf

File Size

179 pages

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