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 …

A Flexible Zero-Inflated Poisson Regression Model, Eric S. Roemmele

Theses and Dissertations--Statistics

A practical problem often encountered with observed count data is the presence of excess zeros. Zero-inflation in count data can easily be handled by zero-inflated models, which is a two-component mixture of a point mass at zero and a discrete distribution for the count data. In the presence of predictors, zero-inflated Poisson (ZIP) regression models are, perhaps, the most commonly used. However, the fully parametric ZIP regression model could sometimes be restrictive, especially with respect to the mixing proportions. Taking inspiration from some of the recent literature on semiparametric mixtures of regressions models for flexible mixture modeling, we propose a …

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 …

Nonparametric Compound Estimation, Derivative Estimation, And Change Point Detection, Sisheng Liu

Theses and Dissertations--Statistics

Firstly, we reviewed some popular nonparameteric regression methods during the past several decades. Then we extended the compound estimation (Charnigo and Srinivasan [2011]) to adapt random design points and heteroskedasticity and proposed a modified Cp criteria for tuning parameter selection. Moreover, we developed a DCp criteria for tuning paramter selection problem in general nonparametric derivative estimation. This extends GCp criteria in Charnigo, Hall and Srinivasan [2011] with random design points and heteroskedasticity. Next, we proposed a change point detection method via compound estimation for both fixed design and random design case, the adaptation of heteroskedasticity was considered for the method. …

Analysis Of Spatial Data, Xiang Zhang

Theses and Dissertations--Statistics

In many areas of the agriculture, biological, physical and social sciences, spatial lattice data are becoming increasingly common. In addition, a large amount of lattice data shows not only visible spatial pattern but also temporal pattern (see, Zhu et al. 2005). An interesting problem is to develop a model to systematically model the relationship between the response variable and possible explanatory variable, while accounting for space and time effect simultaneously.

Spatial-temporal linear model and the corresponding likelihood-based statistical inference are important tools for the analysis of spatial-temporal lattice data. We propose a general asymptotic framework for spatial-temporal linear models and …