Graduate Studies, UNL

 

Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–

First Advisor

Xueheng Shi

Second Advisor

Bertrand Clarke

Degree Name

Doctor of Philosophy (Ph.D.)

Committee Members

Huijing Du, Kent Eskridge, Souparno Ghosh

Department

Statistics

Date of this Version

2025

Document Type

Dissertation

Citation

A dissertation presented to the faculty of the Graduate College of the University of Nebraska in partial fulfillment of requirements for the degree Doctor of Philosophy (Ph.D.)

Major: Statistics

Under the supervision of Professor

Lincoln, Nebraska, December 2025

Comments

Copyright 2025, the author. Used by permission

Abstract

This dissertation presents a general framework for changepoint detection based on $\ell_0$ model selection. The core method, Iteratively Reweighted Fused Lasso (IRFL), improves upon the generalized lasso by adaptively reweighting penalties to enhance support recovery and minimize criteria such as the Bayesian Information Criterion (BIC). The approach allows for flexible modeling of seasonal patterns, linear and quadratic trends, and autoregressive dependence in the presence of changepoints.

Simulation studies demonstrate that IRFL achieves accurate changepoint detection across a wide range of challenging scenarios, including those involving nuisance factors such as trends, seasonal patterns, and serially correlated errors. The framework is further extended to image data, where it enables edge-preserving denoising and segmentation, with applications spanning medical imaging and high-throughput plant phenotyping.

Applications to real-world data demonstrate IRFL’s utility. In particular, analysis of the Mauna Loa CO\textsubscript{2} time series reveals changepoints that align with volcanic eruptions and ENSO events, yielding a more accurate trend decomposition than ordinary least squares. Overall, IRFL provides a robust, extensible tool for detecting structural change in complex data.

Advisors: Xueheng Shi and Bertrand Clarke

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