Statistical Models Commons^™

High Dimensional Data Analysis: Variable Screening And Inference, Lei Fang

Theses and Dissertations--Statistics

This dissertation focuses on the problem of high dimensional data analysis, which arises in many fields including genomics, finance, and social sciences. In such settings, the number of features or variables is much larger than the number of observations, posing significant challenges to traditional statistical methods.

To address these challenges, this dissertation proposes novel methods for variable screening and inference. The first part of the dissertation focuses on variable screening, which aims to identify a subset of important variables that are strongly associated with the response variable. Specifically, we propose a robust nonparametric screening method to effectively select the predictors …

Finite Mixtures Of Mean-Parameterized Conway-Maxwell-Poisson Models, Dongying Zhan

Theses and Dissertations--Statistics

For modeling count data, the Conway-Maxwell-Poisson (CMP) distribution is a popular generalization of the Poisson distribution due to its ability to characterize data over- or under-dispersion. While the classic parameterization of the CMP has been well-studied, its main drawback is that it is does not directly model the mean of the counts. This is mitigated by using a mean-parameterized version of the CMP distribution. In this work, we are concerned with the setting where count data may be comprised of subpopulations, each possibly having varying degrees of data dispersion. Thus, we propose a finite mixture of mean-parameterized CMP distributions. An …