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 …

The Family Of Conditional Penalized Methods With Their Application In Sufficient Variable Selection, Jin Xie

Theses and Dissertations--Statistics

When scientists know in advance that some features (variables) are important in modeling a data, then these important features should be kept in the model. How can we utilize this prior information to effectively find other important features? This dissertation is to provide a solution, using such prior information. We propose the Conditional Adaptive Lasso (CAL) estimates to exploit this knowledge. By choosing a meaningful conditioning set, namely the prior information, CAL shows better performance in both variable selection and model estimation. We also propose Sufficient Conditional Adaptive Lasso Variable Screening (SCAL-VS) and Conditioning Set Sufficient Conditional Adaptive Lasso Variable …