Date of Award
Winter 12-15-2022
Degree Name
Doctor of Philosophy (PhD)
Degree Type
Dissertation
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.
Language
English (en)
Chair and Committee
Nan Lin
Committee Members
José Figueroa-Lopez
Recommended Citation
Rodriguez, Cezareo, "Dealing with Dimensionality: Problems and Techniques in High-Dimensional Statistics" (2022). Arts & Sciences Electronic Theses and Dissertations. 2752.
https://openscholarship.wustl.edu/art_sci_etds/2752