Statistical Models Commons^™

Estimating And Testing Treatment Effects With Misclassified Multivariate Data, Zi Ye

Theses and Dissertations--Statistics

Clinical trials are often used to assess drug efficacy and safety. Participants are sometimes pre-stratified into different groups by diagnostic tools. However, these diagnostic tools are fallible. The traditional method ignores this problem and assumes the diagnostic devices are perfect. This assumption will lead to inefficient and biased estimators. In this era of personalized medicine and measurement-based care, the issues of bias and efficiency are of paramount importance. Despite the prominence, only few researches evaluated the treatment effect in the presence of misclassifications in some special cases and most others focus on assessing the accuracy of the diagnostic devices. In …

Nonparametric Tests Of Lack Of Fit For Multivariate Data, Yan Xu

Theses and Dissertations--Statistics

A common problem in regression analysis (linear or nonlinear) is assessing the lack-of-fit. Existing methods make parametric or semi-parametric assumptions to model the conditional mean or covariance matrices. In this dissertation, we propose fully nonparametric methods that make only additive error assumptions. Our nonparametric approach relies on ideas from nonparametric smoothing to reduce the test of association (lack-of-fit) problem into a nonparametric multivariate analysis of variance. A major problem that arises in this approach is that the key assumptions of independence and constant covariance matrix among the groups will be violated. As a result, the standard asymptotic theory is not …

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 …

Effect Of Socioeconomic And Demographic Factors On Kentucky Crashes, Aaron Berry Cambron

Theses and Dissertations--Civil Engineering

The goal of this research was to examine the potential predictive ability of socioeconomic and demographic data for drivers on Kentucky crash occurrence. Identifying unique background characteristics of at-fault drivers that contribute to crash rates and crash severity may lead to improved and more specific interventions to reduce the negative impacts of motor vehicle crashes. The driver-residence zip code was used as a spatial unit to connect five years of Kentucky crash data with socioeconomic factors from the U.S. Census, such as income, employment, education, age, and others, along with terrain and vehicle age. At-fault driver crash counts, normalized over …

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 …

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 …