Ph.D Thesis Defense: "Three essays on complex dependent data"

Abstract: Statistical analysis of correlated data is undertaken in many practical contexts. In this talk, two types of correlated data are considered: one is the dataset with high-dimensional outcomes; the other is longitudinal data.

I will first talk about a basic problem in modern multivariate analysis, that is, testing the equality of two mean vectors in settings where the dimension p increases with the sample size n. We propose a robust two-sample test for high-dimensional data against sparse and strong alternatives, in which the mean vectors of the populations differ in only a few dimensions, but the magnitude of the differences is large. High-dimensional data are also ubiquitous in genomics. I will talk about the problem of detecting differentially methylated regions using whole-genome bisulfite sequencing and Tet-assisted bisulfite sequencing data to illustrate the challenge of high-dimensionality in the analysis of next-generation sequencing technology.

For longitudinal data, I will introduce method agreement study in medical and clinical fields. We propose a model-based approach to assess agreement of two measuring methods for paired repeated binary measurements. Approaches for assessing method agreement, such as the Bland-Altman diagram and Cohen’s kappa, are also developed for repeated binary measurements based upon the latent variables.

Host: Nan Lin