Date of Award

2025-08-01

Degree Name

Doctor of Philosophy

Department

Mathematical Sciences

Advisor(s)

Xiaogang Su

Abstract

Count data frequently arise in biomedical, economic, and social science research and are often characterized by structural excesses at specific count levels. To accommodate such patterns, Su et al. (2013), among others, introduced the Multiple-Inflation Poisson (MIP) model, which allows for multiple inflated counts within the distribution. However, two critical challenges remain in modeling such data: (i) identifying the true inflation points where excess counts occur, and (ii) selecting the relevant covariates that explain variation in the inflation and count process. This dissertation addresses these issues by advancing the MIP model through a novel methodology that enables the simultaneous selection of inflated count levels and influential predictors. The proposed approach integrates a fused regularization technique with a continuous approximation to the L0-norm, and leverages subtle uprooting penalty Su (2015) to encourage sparsity and enhance model interpretability. Subtle uprooting is a tuning-free penalty, thereby eliminating the need for exhaustive grid searches over tuning parameters and significantly reducing the computational burden common to existing regularized methods. Its formulation as a single-step continuous optimization makes it particularly well-suited for a finite mixture model (FMM) such as the MIP model. Extensive simulation studies confirm the selection consistency and estimation accuracy of the proposed method, demonstrating its ability to recover both the correct inflation structure and associated covariates. The methodology is further applied to a real-world dataset involving doctor visit counts, illustrating its practical efficacy in applied health data analysis. The dissertation concludes by outlining potential extensions to the MIP framework, including its application to longitudinal and spatial count data, and opportunities for integrating post-selection inference and Bayesian techniques.

Language

en

Provenance

Received from ProQuest

File Size

185 p.

File Format

application/pdf

Rights Holder

John Koomson

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