Date of Award
Doctor of Philosophy (PhD)
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.
Chair and Committee
Rodriguez, Cezareo, "Dealing with Dimensionality: Problems and Techniques in High-Dimensional Statistics" (2022). Arts & Sciences Electronic Theses and Dissertations. 2752.