Statistical Models Commons^™

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 …

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 …

Deriving The Distributions And Developing Methods Of Inference For R2-Type Measures, With Applications To Big Data Analysis, Gregory S. Hawk

Theses and Dissertations--Statistics

As computing capabilities and cloud-enhanced data sharing has accelerated exponentially in the 21st century, our access to Big Data has revolutionized the way we see data around the world, from healthcare to investments to manufacturing to retail and supply-chain. In many areas of research, however, the cost of obtaining each data point makes more than just a few observations impossible. While machine learning and artificial intelligence (AI) are improving our ability to make predictions from datasets, we need better statistical methods to improve our ability to understand and translate models into meaningful and actionable insights.

A central goal in the …

Statistical Theory For Specialized Linear Regression Adjustment Methods Compared To Multiple Linear Regression In The Presence And Absence Of Interaction Effects, Leon Su

Theses and Dissertations--Statistics

When building models to investigate outcomes and variables of interest, researchers often want to adjust for other variables. There is a variety of ways that these adjustments are performed. In this work, we will consider four approaches to adjustment utilized by researchers in various fields. We will compare the efficacy of these methods to what we call the ”true model method”, fitting a multiple linear regression model in which adjustment variables are model covariates. Our goal is to show that these adjustment methods have inferior performance to the true model method by comparing model parameter estimates, power, type I error, …

Dimension Reduction Techniques In Regression, Pei Wang

Theses and Dissertations--Statistics

Because of the advances of modern technology, the size of the collected data nowadays is larger and the structure is more complex. To deal with such kinds of data, sufficient dimension reduction (SDR) and reduced rank (RR) regression are two powerful tools. This dissertation focuses on these two tools and it is composed of three projects. In the first project, we introduce a new SDR method through a novel approach of feature filter to recover the central mean subspace exhaustively along with a method to determine the dimension, two variable selection methods, and extensions to multivariate response and large p …

Semiparametric And Nonparametric Methods For Comparing Biomarker Levels Between Groups, Yuntong Li

Theses and Dissertations--Statistics

Comparing the distribution of biomarker measurements between two groups under either an unpaired or paired design is a common goal in many biomarker studies. However, analyzing biomarker data is sometimes challenging because the data may not be normally distributed and contain a large fraction of zero values or missing values. Although several statistical methods have been proposed, they either require data normality assumption, or are inefficient. We proposed a novel two-part semiparametric method for data under an unpaired setting and a nonparametric method for data under a paired setting. The semiparametric method considers a two-part model, a logistic regression for …

Estimation Of The Treatment Effect With Bayesian Adjustment For Covariates, Li Xu

Theses and Dissertations--Statistics

The Bayesian adjustment for confounding (BAC) is a Bayesian model averaging method to select and adjust for confounding factors when evaluating the average causal effect of an exposure on a certain outcome. We extend the BAC method to time-to-event outcomes. Specifically, the posterior distribution of the exposure effect on a time-to-event outcome is calculated as a weighted average of posterior distributions from a number of candidate proportional hazards models, weighing each model by its ability to adjust for confounding factors. The Bayesian Information Criterion based on the partial likelihood is used to compare different models and approximate the Bayes factor. …

Statistical Intervals For Various Distributions Based On Different Inference Methods, Yixuan Zou

Theses and Dissertations--Statistics

Statistical intervals (e.g., confidence, prediction, or tolerance) are widely used to quantify uncertainty, but complex settings can create challenges to obtain such intervals that possess the desired properties. My thesis will address diverse data settings and approaches that are shown empirically to have good performance. We first introduce a focused treatment on using a single-layer bootstrap calibration to improve the coverage probabilities of two-sided parametric tolerance intervals for non-normal distributions. We then turn to zero-inflated data, which are commonly found in, among other areas, pharmaceutical and quality control applications. However, the inference problem often becomes difficult in the presence of …

Transforms In Sufficient Dimension Reduction And Their Applications In High Dimensional Data, Jiaying Weng

Theses and Dissertations--Statistics

The big data era poses great challenges as well as opportunities for researchers to develop efficient statistical approaches to analyze massive data. Sufficient dimension reduction is such an important tool in modern data analysis and has received extensive attention in both academia and industry.

In this dissertation, we introduce inverse regression estimators using Fourier transforms, which is superior to the existing SDR methods in two folds, (1) it avoids the slicing of the response variable, (2) it can be readily extended to solve the high dimensional data problem. For the ultra-high dimensional problem, we investigate both eigenvalue decomposition and minimum …

Composite Nonparametric Tests In High Dimension, Alejandro G. Villasante Tezanos

Theses and Dissertations--Statistics

This dissertation focuses on the problem of making high-dimensional inference for two or more groups. High-dimensional means both the sample size (n) and dimension (p) tend to infinity, possibly at different rates. Classical approaches for group comparisons fail in the high-dimensional situation, in the sense that they have incorrect sizes and low powers. Much has been done in recent years to overcome these problems. However, these recent works make restrictive assumptions in terms of the number of treatments to be compared and/or the distribution of the data. This research aims to (1) propose and investigate refined …

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. …

Improved Models For Differential Analysis For Genomic Data, Hong Wang

Theses and Dissertations--Statistics

This paper intend to develop novel statistical methods to improve genomic data analysis, especially for differential analysis. We considered two different data type: NanoString nCounter data and somatic mutation data. For NanoString nCounter data, we develop a novel differential expression detection method. The method considers a generalized linear model of the negative binomial family to characterize count data and allows for multi-factor design. Data normalization is incorporated in the model framework through data normalization parameters, which are estimated from control genes embedded in the nCounter system. For somatic mutation data, we develop beta-binomial model-based approaches to identify highly or lowly …

Development In Normal Mixture And Mixture Of Experts Modeling, Meng Qi

Theses and Dissertations--Statistics

In this dissertation, first we consider the problem of testing homogeneity and order in a contaminated normal model, when the data is correlated under some known covariance structure. To address this problem, we developed a moment based homogeneity and order test, and design weights for test statistics to increase power for homogeneity test. We applied our test to microarray about Down’s syndrome. This dissertation also studies a singular Bayesian information criterion (sBIC) for a bivariate hierarchical mixture model with varying weights, and develops a new data dependent information criterion (sFLIC).We apply our model and criteria to birth- weight and gestational …

Genetic Association Testing Of Copy Number Variation, Yinglei Li

Theses and Dissertations--Statistics

Copy-number variation (CNV) has been implicated in many complex diseases. It is of great interest to detect and locate such regions through genetic association testings. However, the association testings are complicated by the fact that CNVs usually span multiple markers and thus such markers are correlated to each other. To overcome the difficulty, it is desirable to pool information across the markers. In this thesis, we propose a kernel-based method for aggregation of marker-level tests, in which first we obtain a bunch of p-values through association tests for every marker and then the association test involving CNV is based on …

Normal Mixture And Contaminated Model With Nuisance Parameter And Applications, Qian Fan

Theses and Dissertations--Statistics

This paper intend to find the proper hypothesis and test statistic for testing existence of bilaterally contamination when there exists nuisance parameter. The test statistic is based on method of moments estimators. Union-Intersection test is used for testing if the distribution of population can be implemented by a bilaterally contaminated normal model with unknown variance. This paper also developed a hierarchical normal mixture model (HNM) and applied it to birth weight data. EM algorithm is employed for parameter estimation and a singular Bayesian information criterion (sBIC) is applied to choose the number components. We also proposed a singular flexible information …

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 …