Multivariate Analysis Commons^™

Nonparametric Derivative Estimation Using Penalized Splines: Theory And Application, Bright Antwi Boasiako

Doctoral Dissertations

This dissertation is in the field of Nonparametric Derivative Estimation using
Penalized Splines. It is conducted in two parts. In the first part, we study the L2
convergence rates of estimating derivatives of mean regression functions using penalized splines. In 1982, Stone provided the optimal rates of convergence for estimating derivatives of mean regression functions using nonparametric methods. Using these rates, Zhou et. al. in their 2000 paper showed that the MSE of derivative estimators based on regression splines approach zero at the optimal rate of convergence. Also, in 2019, Xiao showed that, under some general conditions, penalized spline estimators …

Monitoring Mammals At Multiple Scales: Case Studies From Carnivore Communities, Kadambari Devarajan

Doctoral Dissertations

Carnivores are distributed widely and threatened by habitat loss, poaching, climate change, and disease. They are considered integral to ecosystem function through their direct and indirect interactions with species at different trophic levels. Given the importance of carnivores, it is of high conservation priority to understand the processes driving carnivore assemblages in different systems. It is thus essential to determine the abiotic and biotic drivers of carnivore community composition at different spatial scales and address the following questions: (i) What factors influence carnivore community composition and diversity? (ii) How do the factors influencing carnivore communities vary across spatial and temporal …

Model-Free Descriptive Modeling For Multivariate Categorical Data With An Ordinal Dependent Variable, Li Wang

Doctoral Dissertations

In the process of statistical modeling, the descriptive modeling plays an essential role in accelerating the formulation of plausible hypotheses in the subsequent explanatory modeling and facilitating the selection of potential variables in the subsequent predictive modeling. Especially, for multivariate categorical data analysis, it is desirable to use the descriptive modeling methods for uncovering and summarizing the potential association structure among multiple categorical variables in a compact manner. However, many classical methods in this case either rely on strong assumptions for parametric models or become infeasible when the data dimension is higher. To this end, we propose a model-free method …

Bayesian Methods For The Assessment Of Reporting Errors For Data-Sparse Population-Periods With Applications To Estimating Mortality, Emily Peterson

Doctoral Dissertations

Population level mortality data is often subject to substantial reporting errors due to misclassification of cause of death, misclassification of death status, or age reporting errors. Accuracy of error-prone data sources can be assessed by comparing such data to gold standard data for the same population-period. We present Bayesian methods for assessing the extent of reporting errors across different population-periods and generalizing those to settings where gold-standard data are lacking. Firstly, we investigate misclassification errors of maternal cause of death reporting in civil registration vital statistics data. We use a Bayesian hierarchical bivariate random-walk model to estimate country-year specific sensitivity …

Nanoindentation Characterization Of Elastic Properties Of Shales And Swelling Clay Minerals, Shengmin Luo

Doctoral Dissertations

Oil and gas shales are a class of multiscale, multiphase, hybrid inorganic-organic sedimentary rocks that consist of a generally uniform, preferentially oriented clay matrix with randomly embedded silt and sand particles as solid inclusions. A thorough understanding of the mechanical properties of shales is crucial for the exploration and production of oil and gas in the unconventional shale reservoirs, but it can be a challenging task due to their nature of compositional heterogeneity and microstructural anisotropy. In efforts to better characterize the mechanical properties of shales across different length scales and to fundamentally understand the laws of upscaling from individual …

Regression Analysis For Ordinal Outcomes In Matched Study Design: Applications To Alzheimer's Disease Studies, Elizabeth Austin

Masters Theses

Alzheimer's Disease (AD) affects nearly 5.4 million Americans as of 2016 and is the most common form of dementia. The disease is characterized by the presence of neurofibrillary tangles and amyloid plaques [1]. The amount of plaques are measured by Braak stage, post-mortem. It is known that AD is positively associated with hypercholesterolemia [16]. As statins are the most widely used cholesterol-lowering drug, there may be associations between statin use and AD. We hypothesize that those who use statins, specifically lipophilic statins, are more likely to have a low Braak stage in post-mortem analysis.

In order to address this hypothesis, …

Statistical Methods On Risk Management Of Extreme Events, Zijing Zhang

Doctoral Dissertations

The goal of the dissertation is the investigation of financial risk analysis methodologies, using the schemes for extreme value modeling as well as techniques from copula modeling. Extreme value theory is concerned with probabilistic and statistical questions re- lated to unusual behavior or rare events. The subject has a rich mathematical theory and also a long tradition of applications in a variety of areas. We are interested in its application in risk management, with a focus on estimating and forcasting the Value-at-Risk of financial time series data. Extremal data are inherently scarce, thus making inference challenging. In order to obtain …

Variable Selection In Single Index Varying Coefficient Models With Lasso, Peng Wang

Doctoral Dissertations

Single index varying coefficient model is a very attractive statistical model due to its ability to reduce dimensions and easy-of-interpretation. There are many theoretical studies and practical applications with it, but typically without features of variable selection, and no public software is available for solving it. Here we propose a new algorithm to fit the single index varying coefficient model, and to carry variable selection in the index part with LASSO. The core idea is a two-step scheme which alternates between estimating coefficient functions and selecting-and-estimating the single index. Both in simulation and in application to a Geoscience dataset, we …

Spatial And Temporal Correlations Of Freeway Link Speeds: An Empirical Study, Piotr J. Rachtan

Masters Theses 1911 - February 2014

Congestion on roadways and high level of uncertainty of traffic conditions are major considerations for trip planning. The purpose of this research is to investigate the characteristics and patterns of spatial and temporal correlations and also to detect other variables that affect correlation in a freeway setting. 5-minute speed aggregates from the Performance Measurement System (PeMS) database are obtained for two directions of an urban freeway – I-10 between Santa Monica and Los Angeles, California. Observations are for all non-holiday weekdays between January 1st and June 30th, 2010. Other variables include traffic flow, ramp locations, number of lanes and the …