Date of Award

12-24-2025

Date Published

January 2026

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Advisor(s)

Hyune-Ju Kim

Keywords

Bayes Information Criterion;Change-point;Lasso;Model selection;Segmented logistic regression

Abstract

This dissertation investigates the problem of change-point detection in segmented logistic regression models, where the total number of change-points is unknown. We consider both unconstrained models, which allow discontinuities at change-points, and constrained models, which impose continuity across change-points. The central challenge is to determine the number of change-points and to accurately estimate their locations, while ensuring valid statistical inference for the associated regression coefficients. We begin by introducing a set of regularity assumptions that underlie the theoretical analysis throughout this work. For a given number of change-points, we present algorithms to estimate their locations and obtain the maximum likelihood function. From a model selection perspective, we establish the consistency of change-point number estimation by BIC-type criteria under both unconstrained and constrained models. In addition, we derive the convergence rate of the estimated change-points when the selected number is at least as large as the true number, and prove the asymptotic normality of the regression coefficients when the true number of change-points is correctly identified. Simulation studies are carried out to validate and illustrate the theoretical results. In addition to information-criteria-based approaches, we apply Lasso-type estimators for changepoint selection. We propose a fitting procedure that includes a pre-selection step, thereby reducing the change-point Lasso regression problem to a low-dimensional setting. Under appropriate conditions on the covariates, we establish the consistency of model selection. Finally, simulation studies compare the performance of BIC-type criteria and Lasso in model selection and provide practical guidance on choosing the regularization parameter λ.

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Open Access

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