Statistical Methodology Commons^™

Compare And Contrast Maximum Likelihood Method And Inverse Probability Weighting Method In Missing Data Analysis, Scott Sun

Mathematical Sciences Technical Reports (MSTR)

Data can be lost for different reasons, but sometimes the missingness is a part of the data collection process. Unbiased and efficient estimation of the parameters governing the response mean model requires the missing data to be appropriately addressed. This paper compares and contrasts the Maximum Likelihood and Inverse Probability Weighting estimators in an Outcome-Dependendent Sampling design that deliberately generates incomplete observations. WE demonstrate the comparison through numerical simulations under varied conditions: different coefficient of determination, and whether or not the mean model is misspecified.

Characterizing The Northern Hemisphere Circumpolar Vortex Through Space And Time, Nazla Bushra

LSU Doctoral Dissertations

This hemispheric-scale, steering atmospheric circulation represented by the circumpolar vortices (CPVs) are the middle- and upper-tropospheric wind belts circumnavigating the poles. Variability in the CPV area, shape, and position are important topics in geoenvironmental sciences because of the many links to environmental features. However, a means of characterizing the CPV has remained elusive. The goal of this research is to (i) identify the Northern Hemisphere CPV (NHCPV) and its morphometric characteristics, (ii) understand the daily characteristics of NHCPV area and circularity over time, (iii) identify and analyze spatiotemporal variability in the NHCPV’s centroid, and (iv) analyze how CPV features relate …

Guidelines For Regression Analysis In Sas And R: A Case Study, Sarah Milligan

Honors Program Theses and Projects

When a player is a free agent, an individual who is able to sign to any team, one wonders what their best option is. Will signing with Team A or Team B provide them with the largest salary? What factors will affect their salary the most? Does last year’s statistics have a strong impact on next year’s salary? These questions can be answered by performing a regression analysis on previous years data. The primary focus of this project is to determine the most important variables related to an NBA salary. Likewise, the statistical programs SAS and R will be compared …

Cointegration And Statistical Arbitrage Of Precious Metals, Judge Van Horn

Finance Undergraduate Honors Theses

When talking about financial instruments correlation is often thrown around as a measure of the relation between two securities. An often more useful or tradeable measure is cointegration. Cointegration is the measure of two securities tendency to revert to an average price over time. In other words, cointegration ignores directionality and only cares about the distance between two securities. For a mean reversion strategy such as statistical arbitrage cointegration proves to be a far more reliable statistical measure of mean reversion, and while it is more reliable than correlation it still has its own problems. One thing to consider is …

Markov Chains And Their Applications, Fariha Mahfuz

Math Theses

Markov chain is a stochastic model that is used to predict future events. Markov chain is relatively simple since it only requires the information of the present state to predict the future states. In this paper we will go over the basic concepts of Markov Chain and several of its applications including Google PageRank algorithm, weather prediction and gamblers ruin.

We examine on how the Google PageRank algorithm works efficiently to provide PageRank for a Google search result. We also show how can we use Markov chain to predict weather by creating a model from real life data.

Comparing Radiation Shielding Potential Of Liquid Propellants To Water For Application In Space, John Czaplewski

Master's Theses

The radiation environment in space is a threat that engineers and astronauts need to mitigate as exploration into the solar system expands. Passive shielding involves placing as much material between critical components and the radiation environment as possible. However, with mass and size budgets, it is important to select efficient materials to provide shielding. Currently, NASA and other space agencies plan on using water as a shield against radiation since it is already necessary for human missions. Water has been tested thoroughly and has been proven to be effective. Liquid propellants are needed for every mission and also share similar …

Sars-Cov-2 Pandemic Analytical Overview With Machine Learning Predictability, Anthony Tanaydin, Jingchen Liang, Daniel W. Engels

SMU Data Science Review

Understanding diagnostic tests and examining important features of novel coronavirus (COVID-19) infection are essential steps for controlling the current pandemic of 2020. In this paper, we study the relationship between clinical diagnosis and analytical features of patient blood panels from the US, Mexico, and Brazil. Our analysis confirms that among adults, the risk of severe illness from COVID-19 increases with pre-existing conditions such as diabetes and immunosuppression. Although more than eight months into pandemic, more data have become available to indicate that more young adults were getting infected. In addition, we expand on the definition of COVID-19 test and discuss …

Evaluation Of The Effect Of The Clinical-Decision-Support Systems On Diabetes Management: A Multivariate Meta-Analysis Comparison With Univariate Meta-Analysis, Abdelfattah Elbarsha

Electronic Theses and Dissertations

The advantage of using meta-analysis lies in its ability in providing a quantitative summary of the findings from multiple studies. The aim of this dissertation was first to conduct a simulation study in order to understand what factors (sample size, between-study correlation, and percent of missing data) have a significant effect on meta-analysis estimates and whether using univariate or multivariate meta-analysis would produce different estimates.

The second goal of this study was to evaluate the effect of clinical decision support systems CDSS on diabetes care management by conducting three separate univariate meta-analyses and one multivariate meta-analysis. CDSS are health information …

The Combined Impact Of Continuous And Ordinal Auxiliary Variables On Missing Data Imputation In Sem, Salina Wu Whitaker

Electronic Theses and Dissertations

“Modern” methods of addressing missing data using full-information maximum-likelihood (FIML) have become mainstays in SEM analyses. FIML allows the inclusion of auxiliary variables which carry information that is related to missing values and can reduce bias in parameter estimates. Past research has illustrated the benefits of auxiliary variable inclusion under different missingness conditions (MCAR and MNAR; e.g., Enders, 2008), missingness proportions (e.g., Collins et al., 2001), and although limited, missingness patterns (e.g., Yoo, 2009) in FIML analyses. While past studies have focused on the effects of either continuous or ordinal auxiliary variables, no study has included both types in their …

Novel Statistical Analysis In The Context Of A Comprehensive Needs Assessment For Secondary Stem Recruitment, Norou Diawara, Sarah Ferguson, Melva Grant, Kumer Das

Mathematics & Statistics Faculty Publications

There is a myriad of career opportunities stemming from science, technology, engineering, and mathematics (STEM) disciplines. In addition to careers in corporate settings, teaching is a viable career option for individuals pursuing degrees in STEM disciplines. With national shortages of secondary STEM teachers, efforts to recruit, train, and retain quality STEM teachers is greatly important. Prior to exploring ways to attract potential STEM teacher candidates to pursue teacher training programs, it is important to understand the perceived value that potential recruits place on STEM careers, disciplines, and the teaching profession. The purpose of this study was to explore students’ perceptions …

A Class Of Copula-Based Bivariate Poisson Time Series Models With Applications, Mohammed Alqawba, Dimuthu Fernando, Norou Diawara

Mathematics & Statistics Faculty Publications

A class of bivariate integer-valued time series models was constructed via copula theory. Each series follows a Markov chain with the serial dependence captured using copula-based transition probabilities from the Poisson and the zero-inflated Poisson (ZIP) margins. The copula theory was also used again to capture the dependence between the two series using either the bivariate Gaussian or “t-copula” functions. Such a method provides a flexible dependence structure that allows for positive and negative correlation, as well. In addition, the use of a copula permits applying different margins with a complicated structure such as the ZIP distribution. Likelihood-based inference was …

Statistical Approaches For Estimation And Comparison Of Brain Functional Connectivity, Jifang Zhao

Theses and Dissertations

Drug addiction can lead to many health-related problems and social concerns. Functional connectivity obtained from functional magnetic resonance imaging (fMRI) data promotes a variety of fundamental understandings in such association. Due to its complex correlation structure and large dimensionality, the modeling and analysis of the functional connectivity from neuroimage are challenging. By proposing a spatio-temporal model for multi-subject neuroimage data, we incorporate voxel-level spatio-temporal dependencies of whole-brain measurements to improve the accuracy of statistical inference. To tackle large-scale spatio-temporal neuroimage data, we develop a computationally efficient algorithm to estimate the parameters. Our method is used to identify functional connectivity and …

Investigations Into The Genetics Of Mixed Pathologies In Dementia, Adam Dugan

Theses and Dissertations--Epidemiology and Biostatistics

Alzheimer’s disease (AD) is an irreversible, progressive brain disorder that leads to a loss of memory and thinking skills. While tremendous progress has been made in our understanding of the genetics underlying AD, currently known genetic variants explain only approximately 30% of the heritable risk of developing AD. One hurdle to AD research is that it can only be definitively diagnosed at autopsy, making cruder, clinic-based diagnoses more common. In recent years, several brain pathologies that mimic AD’s clinical presentation have been identified including brain arteriolosclerosis, hippocampal sclerosis (HS), and, most recently, limbic-predominant age-related TDP-43 encephalopathy (LATE). It has become …

Addressing The Ecological Fallacy With Lagrangian Inference, Michael Schwob

Calvert Undergraduate Research Awards

Most epidemiologists elect to use statistical models that use population-level data to make inference on the spread of some virus or disease. This has become commonplace in the fields of epidemiology and biostatistics since most data used to construct and verify epidemic models are recorded at the population-level. Obtaining inference from a population-level model may be beneficial in studying the spread of disease in a homogeneous population, but the use of such models to describe a heterogeneous population results in inadequate inference. The inaccuracy of these models is further amplified when one tries to make individual-level inference from these population-level …

An Evaluation Of Knot Placement Strategies For Spline Regression, William Klein

CMC Senior Theses

Regression splines have an established value for producing quality fit at a relatively low-degree polynomial. This paper explores the implications of adopting new methods for knot selection in tandem with established methodology from the current literature. Structural features of generated datasets, as well as residuals collected from sequential iterative models are used to augment the equidistant knot selection process. From analyzing a simulated dataset and an application onto the Racial Animus dataset, I find that a B-spline basis paired with equally-spaced knots remains the best choice when data are evenly distributed, even when structural features of a dataset are known …

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 …

Novel Nonparametric Testing Approaches For Multivariate Growth Curve Data: Finite-Sample, Resampling And Rank-Based Methods, Ting Zeng

Theses and Dissertations--Statistics

Multivariate growth curve data naturally arise in various fields, for example, biomedical science, public health, agriculture, social science and so on. For data of this type, the classical approach is to conduct multivariate analysis of variance (MANOVA) based on Wilks' Lambda and other multivariate statistics, which require the assumptions of multivariate normality and homogeneity of within-cell covariance matrices. However, data being analyzed nowadays show marked departure from multivariate normal distribution and homoscedasticity. In this dissertation, we investigate nonparametric testing approaches for multivariate growth curve data from three aspects, i.e., finite-sample, resampling and rank-based methods.

The first project proposes an approximate …

Statistical Methods In Genetic Studies, Cheng Gao

Dissertations, Master's Theses and Master's Reports

This dissertation includes three Chapters. A brief description of each chapter is organized as follows.

In Chapter 1, we proposed a new method, called MF-TOWmuT, for genome-wide association studies with multiple genetic variants and multiple phenotypes using family samples. MF-TOWmuT uses kinship matrix to account for sample relatedness. It is worth mentioning that in simulations, we considered hidden polygenic effects and varied the proportion of variance contributed by it to generate phenotypes. Simulation studies show that MF-TOWmuT can preserve the type I error rates and is more powerful than several existing methods in different simulation scenarios, MFTOWmuT is also quite …

Comparing Various Robust Estimation Techniques In Regression Analysis, Tracy S. Morrison

All Graduate Theses, Dissertations, and Other Capstone Projects

In regression analysis, the use of the ordinary least squares (OLS) method is inadvisable when dealing with outlier or extreme observations. As a result, we require a method of robust estimation in which the estimation value is not significantly affected by outlier or extreme observations. Four methods of estimation will be compared in this paper in order to determine the best estimation: the M estimation method, the Least Trimmed Square Estimator, the S-estimation method, and the MM estimation method in robust regression. We discover that the best method is the MM-estimation method in this study. The M-estimation method is an …

Innovative Statistical Models In Cancer Immunotherapy Trial Design, Jing Wei

Theses and Dissertations--Statistics

A challenge arising in cancer immunotherapy trial design is the presence of non-proportional hazards (NPH) patterns in survival curves. We considered three different NPH patterns caused by delayed treatment effect, cure rate and responder rate of treatment group in this dissertation. These three NPH patterns would violate the proportional hazard model assumption and ignoring any of them in an immunotherapy trial design will result in substantial loss of statistical power.

In this dissertation, four models to deal with NPH patterns are discussed. First, a piecewise proportional hazards model is proposed to incorporate delayed treatment effect into the trial design consideration. …