Abstract
In modern data analysis, problems involving high dimensional data with more variables than subjects is increasingly common. Two such cases are mediation analysis and distributed optimization. In Chapter 2 we start with an overview of high dimensional statistics and mediation analysis. In Chapter 3 we motivate and prove properties for a new marginal screening procedure for performing high dimensional mediation analysis. This screening procedure is shown via simulation to perform better than benchmark approaches and is applied to a DNA methylation study. In Chapter 4 we construct a cryptosystem that accurately performs distributed penalized quantile regression in the high-dimensional setting using a divide-and-conquer approach while preserving the privacy of subject data.
Committee Chair
Nan Lin
Committee Members
José Figueroa-Lopez
Degree
Doctor of Philosophy (PhD)
Author's Department
Statistics
Document Type
Dissertation
Date of Award
Winter 12-15-2022
Language
English (en)
DOI
https://doi.org/10.7936/99rq-sa77
Recommended Citation
Rodriguez, Cezareo, "Dealing with Dimensionality: Problems and Techniques in High-Dimensional Statistics" (2022). Arts & Sciences Theses and Dissertations. 2752.
The definitive version is available at https://doi.org/10.7936/99rq-sa77