Advanced High Dimensional Regression Techniques

Author

Yuan YangFollow

Date of Award

8-2022

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

School of Mathematical and Statistical Sciences

Committee Chair/Advisor

Dr. Christopher S. McMahan

Committee Member

Dr. Yu-Bo Wang

Committee Member

Dr. Deborah Kunkel

Committee Member

Dr. Xinyi Li

Abstract

This dissertation focuses on developing high dimensional regression techniques to analyze large scale data using both Bayesian and frequentist approaches, motivated by data sets from various disciplines, such as public health and genetics. More specifically, Chapters 2 and Chapter 4 take a Bayesian approach to achieve modeling and parameter estimation simultaneously while Chapter 3 takes a frequentist approach. The main aspects of these techniques are that they perform variable selection and parameter estimation simultaneously, while also being easily adaptable to large-scale data. In particular, by embedding a logistic model into traditional spike and slab framework and selecting of proper prior distributions, we allow for information injection from side information to guide variable selection. Moreover, we simplify the NP-hard non-convex l₀ problem to a weighted LASSO problem by using an approximation to the l₀ norm and Generalized Double Pareto (GDP) shrinkage prior collectively. The finite sample performance of our techniques are investigated using extensive numerical simulation studies that are based on the motivating data sets. The methods are then applied to our motivating data sets including human disease surveillance studies, and genetics.

Recommended Citation

Yang, Yuan, "Advanced High Dimensional Regression Techniques" (2022). All Dissertations. 3144.
https://open.clemson.edu/all_dissertations/3144