Author ORCID Identifier

Date Available


Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation


Arts and Sciences



First Advisor

Dr. Derek Young


Among statistical intervals, confidence intervals and prediction intervals are well-known and commonly used. In many applications, the problem becomes finding an interval that covers at least a certain proportion $P$ of the population for a characteristic of interest with a specified confidence level $(1-\alpha)$. And such interval is named a $P$-content, $(1-\alpha)$-confidence Tolerance Interval (TI). The topic of the dissertation is the utility of tolerance intervals for various regression models. We begin with a discussion of tolerance intervals for linear and nonlinear regression models. We then propose a bootstrap method of constructing TIs for Tobit regression to deal with censored data. Next, we introduce TIs for simple and multiple isotonic regression. Simulation results and application to real data sets are presented respectively to help visualize these regression TIs and to demonstrate that the methods we discuss have coverage probabilities close to the specified nominal confidence level.

Digital Object Identifier (DOI)

Available for download on Friday, August 08, 2025