Date of Award

Summer 2025

Document Type

Open Access Dissertation

Department

Statistics

First Advisor

Xianzheng Huang

Abstract

Regression is a ubiquitous and fundamental method that can be found in any ele- mentary statistics course. The simplicity and self evidently useful nature of linear regression beguiles a non-negligible portion of researchers into disrespecting assump- tions required by these models, namely in terms of accuracy of covariates and the underlying nature of the data. This disregard can at best lead to meaningless results and at worse cause significant misunderstandings in scientific pursuit.

In this dissertation we strive propose remedies to violations of specific assump- tions. Namely the assumptions that covariates are either observed without measure- ment error or they are assumed to be non-periodic, or that responses are non-periodic. Further, we cover the case in which the measurement error is not only present but is non-Gaussian, as is the standard in the majority of measurement error literature. We propose these approaches for not only parametric, but non-parametric regression as well, and introduce a new concept regression with periodic covariates, that is the concept of symmetric responses around a mode. Each of these adaptations serve to better model the response data, which is shown through extensive simulation and real data application.

Rights

© 2025, Nicholas W. Woolsey

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