Author ORCID Identifier
Date Available
8-8-2025
Year of Publication
2023
Document Type
Doctoral Dissertation
Degree Name
Doctor of Philosophy (PhD)
College
Arts and Sciences
Department/School/Program
Statistics
Advisor
Dr. Derek Young
Abstract
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)
https://doi.org/10.13023/etd.2023.360
Recommended Citation
Zhou, Xitong, "Tolerance Intervals for Various Regression Models" (2023). Theses and Dissertations--Statistics. 68.
https://uknowledge.uky.edu/statistics_etds/68
