Physical Sciences and Mathematics Commons^™

A Multi-Indexed Logistic Model For Time Series, Xiang Liu

Electronic Theses and Dissertations

In this thesis, we explore a multi-indexed logistic regression (MILR) model, with particular emphasis given to its application to time series. MILR includes simple logistic regression (SLR) as a special case, and the hope is that it will in some instances also produce significantly better results. To motivate the development of MILR, we consider its application to the analysis of both simulated sine wave data and stock data. We looked at well-studied SLR and its application in the analysis of time series data. Using a more sophisticated representation of sequential data, we then detail the implementation of MILR. We compare …

Tornado Density And Return Periods In The Southeastern United States: Communicating Risk And Vulnerability At The Regional And State Levels, Michelle Bradburn

Electronic Theses and Dissertations

Tornado intensity and impacts vary drastically across space, thus spatial and statistical analyses were used to identify patterns of tornado severity in the Southeastern United States and to assess the vulnerability and estimated recurrence of tornadic activity. Records from the Storm Prediction Center's tornado database (1950-2014) were used to estimate kernel density to identify areas of high and low tornado frequency at both the regional- and state-scales. Return periods (2-year, 5-year, 10-year, 25-year, 50-year, and 100-year) were calculated at both scales as well using a composite score that included EF-scale magnitude, injury counts, and fatality counts. Results showed that the …

Newsvendor Models With Monte Carlo Sampling, Ijeoma W. Ekwegh

Electronic Theses and Dissertations

Newsvendor Models with Monte Carlo Sampling by Ijeoma Winifred Ekwegh The newsvendor model is used in solving inventory problems in which demand is random. In this thesis, we will focus on a method of using Monte Carlo sampling to estimate the order quantity that will either maximizes revenue or minimizes cost given that demand is uncertain. Given data, the Monte Carlo approach will be used in sampling data over scenarios and also estimating the probability density function. A bootstrapping process yields an empirical distribution for the order quantity that will maximize the expected profit. Finally, this method will be used …

Spatio-Temporal Analysis Of Point Patterns, Abdul-Nasah Soale

Electronic Theses and Dissertations

In this thesis, the basic tools of spatial statistics and time series analysis are applied to the case study of the earthquakes in a certain geographical region and time frame. Then some of the existing methods for joint analysis of time and space are described and applied. Finally, additional research questions about the spatial-temporal distribution of the earthquakes are posed and explored using statistical plots and models. The focus in the last section is in the relationship between number of events per year and maximum magnitude and its effect on how clustered the spatial distribution is and the relationship between …

Multilevel Models For Longitudinal Data, Aastha Khatiwada

Electronic Theses and Dissertations

Longitudinal data arise when individuals are measured several times during an ob- servation period and thus the data for each individual are not independent. There are several ways of analyzing longitudinal data when different treatments are com- pared. Multilevel models are used to analyze data that are clustered in some way. In this work, multilevel models are used to analyze longitudinal data from a case study. Results from other more commonly used methods are compared to multilevel models. Also, comparison in output between two software, SAS and R, is done. Finally a method consisting of fitting individual models for each …

Propensity Score Based Methods For Estimating The Treatment Effects Based On Observational Studies., Younathan Abdia

Electronic Theses and Dissertations

This dissertation consists of two interconnected research projects. The first project was a study of propensity scores based statistical methods for estimating the average treatment effect (ATE) and the average treatment effect among treated (ATT) when there are two treatment groups. The ATE is defined as the mean of the individual causal effects in the whole population, while ATT is defined as the treatment effect for the treated population. Propensity score based statistical methods, such as matching, regression, stratification, inverse probability weighting (IPW), and doubly robust (DR) methods were used to estimate the ATE and ATT. Simulation studies and case …

Semi-Parametric Methods For Personalized Treatment Selection And Multi-State Models., Chathura K. Siriwardhana

Electronic Theses and Dissertations

This dissertation contains three research projects on personalized medicine and a project on multi-state modelling. The idea behind personalized medicine is selecting the best treatment that maximizes interested clinical outcomes of an individual based on his or her genetic and genomic information. We propose a method for treatment assignment based on individual covariate information for a patient. Our method covers more than two treatments and it can be applied with a broad set of models and it has very desirable large sample properties. An empirical study using simulations and a real data analysis show the applicability of the proposed procedure. …

Integrated Analysis Of Mirna/Mrna Expression And Gene Methylation Using Sparse Canonical Correlation Analysis., Dake Yang

Electronic Theses and Dissertations

MicroRNAs (miRNAs) are a large number of small endogenous non-coding RNA molecules (18-25 nucleotides in length) which regulate expression of genes post-transcriptionally. While a variety of algorithms exist for determining the targets of miRNAs, they are generally based on sequence information and frequently produce lists consisting of thousands of genes. Canonical correlation analysis (CCA) is a multivariate statistical method that can be used to find linear relationships between two data sets, and here we apply CCA to find the linear combination of differentially expressed miRNAs and their corresponding target genes having maximal negative correlation. Due to the high dimensionality, sparse …

Propensity Score Methods : A Simulation And Case Study Involving Breast Cancer Patients., John Craycroft

Electronic Theses and Dissertations

Observational data presents unique challenges for analysis that are not encountered with experimental data resulting from carefully designed randomized controlled trials. Selection bias and unbalanced treatment assignments can obscure estimations of treatment effects, making the process of causal inference from observational data highly problematic. In 1983, Paul Rosenbaum and Donald Rubin formalized an approach for analyzing observational data that adjusts treatment effect estimates for the set of non-treatment variables that are measured at baseline. The propensity score is the conditional probability of assignment to a treatment group given the covariates. Using this score, one may balance the covariates across treatment …

A Log Rank Test For Clustered Data Under Informative Within-Cluster Group Size., Mary Elizabeth Gregg

Electronic Theses and Dissertations

The log rank test is a popular nonparametric test for comparing the marginal survival distribution of two groups. When data are organized within clusters and the size of clusters or the distribution of group membership within a cluster is related to an outcome of interest, traditional methods of data analysis can be biased. In this thesis, we develop a within-cluster group weighted log rank test to compare marginal survival time distributions between groups from clustered data, correcting for cluster size and intra-cluster group size informativeness. The performance of this new test is compared with the unweighted and cluster-weighted log rank …

Some Contributions To Nonparametric And Semiparametric Inference For Clustered And Multistate Data., Sandipan Dutta

Electronic Theses and Dissertations

This dissertation is composed of research projects that involve methods which can be broadly classified as either nonparametric or semiparametric. Chapter 1 provides an introduction of the problems addressed in these projects, a brief review of the related works that have done so far, and an outline of the methods developed in this dissertation. Chapter 2 describes in details the first project which aims at developing a rank-sum test for clustered data where an outcome from group in a cluster is associated with the number of observations belonging to that group in that cluster. Chapter 3 proposes the use of …

Inference For A Zero-Inflated Conway-Maxwell-Poisson Regression For Clustered Count Data., Hyoyoung Choo-Wosoba

Electronic Theses and Dissertations

This dissertation is directed toward developing a statistical methodology with applications of the Conway-Maxwell-Poisson (CMP) distribution (Conway, R. W., and Maxwell, W. L., 1962) to count data. The count data for this dissertation exhibit three different characteristics: clustering, zero inflation, and dispersion. Clustering suggests that observations within clusters are correlated, and the zero inflation phenomenon occurs when the data exhibit excessive zero counts. Dispersion implies that the mean is greater/smaller than the variance unlike a Poisson distribution. The dissertation starts with an introduction of inference for a zero-inflated clustered count data in the first chapter. Then, it presents novel methodologies …

Takens Theorem With Singular Spectrum Analysis Applied To Noisy Time Series, Thomas K. Torku

Electronic Theses and Dissertations

The evolution of big data has led to financial time series becoming increasingly complex, noisy, non-stationary and nonlinear. Takens theorem can be used to analyze and forecast nonlinear time series, but even small amounts of noise can hopelessly corrupt a Takens approach. In contrast, Singular Spectrum Analysis is an excellent tool for both forecasting and noise reduction. Fortunately, it is possible to combine the Takens approach with Singular Spectrum analysis (SSA), and in fact, estimation of key parameters in Takens theorem is performed with Singular Spectrum Analysis. In this thesis, we combine the denoising abilities of SSA with the Takens …

A Descriptive Study Of The Effect Of Payer Source On Multiple Longitudinal Outcome Measures Within The Tbi Model Systems National Database Using Longitudinal Hlm Analyses, Melissa Carole Hofmann

Electronic Theses and Dissertations

Using longitudinal data from the TBIMS ND, this study utilized a longitudinal hierarchical linear modeling approach to describe the effect of primary payer source on individual level change in outcomes including the FIM and DRS. To facilitate the use of parametric statistics, Rasch-transformed FIM and DRS scores were utilized; thus approaching an interval level of measurement. The FIM was separated into 3 separate cognitive, mobility, and self-care subscales. In this way, rehabilitation professionals including speech, physical, and occupational therapists for this TBI sample could reference results to inform current clinical practice.

Results indicated that FIM and DRS trajectories were best …

A Comparison Of Latent Class Analysis And The Mixture Rasch Model: A Cross-Cultural Comparison Of 8th Grade Mathematics Achievement In The Fourth International Mathematics And Science Study (Timss-2011), Turker Toker

Electronic Theses and Dissertations

This study provides a comparison of the results of latent class analysis (LCA) and mixture Rasch model (MRM) analysis using data from the Trends in International Mathematics and Science Study - 2011 (TIMSS-2011) with a focus on the 8th-grade mathematics section. The research study focuses on the comparison of LCA with Mplus version 7.31 and MRM with WinMira 2011 to determine if results obtained differ when the assumed psychometric model differs. Also, a log-linear analysis was conducted to understand the interactions between latent classes identified by LCA and MRM. The data set used in the study was from four diverse …

A Comparison Between Propensity Score Matching, Weighting, And Stratification In Multiple Treatment Groups: A Simulation Study, Priyalatha Govindasamy

Electronic Theses and Dissertations

The application of propensity score techniques (matching, stratification, and weighting) with multiple treatment levels are similar to those used in binary groups. However, given that the application of propensity scores in multiple treatment groups is new, factors affecting the performance of matching, stratification, and weighting in multiple treatment groups are less explored. Therefore, this study was conducted to determine the performance of different propensity score techniques with multiple treatment groups under various circumstances. Specifically, the study focused on examining how the three propensity score corrective techniques perform in estimating treatment effects under (1) overt and (2) hidden types of selection …

Anatomy, Implant Selection And Placement Influence Spine Mechanics Associated With Total Disc Replacement, Justin F.M. Hollenbeck

Electronic Theses and Dissertations

Through aging and injury, the intervertebral disc of the lumbar spine can undergo degeneration, leading to collapse of the vertebrae and low back pain, a symptom that affects half the adult population in any given year. In an effort to reduce low back pain, total disc replacement treatment removes the degenerated disc, restores natural height and lordosis of the segment, and preserves motion at the joint. Patient anatomy, implant selection, and implant placement play significant roles in a patient's outcomes after total disc replacement surgery. Thus, the objective of the work presented in this thesis was to develop a suite …

Missing Data In Clinical Trial: A Critical Look At The Proportionality Of Mnar And Mar Assumptions For Multiple Imputation, Theophile B. Dipita

Electronic Theses and Dissertations

Randomized control trial is a gold standard of research studies. Randomization helps reduce bias and infer causality. One constraint of these studies is that it depends on participants to obtain the desired data. Whatever the researcher can do, there is a possibility to end up with incomplete data. The problem is more relevant in clinical trials when missing data can be related to the condition under study. The benefits of randomization is compromised by missing data. Multiple imputation is a valid method of treating missing data under the assumption of MAR. Unfortunately this is an unverified assumptions. Current practice advise …

Identifying Data Centers From Satellite Imagery, Adam Buskirk

Electronic Theses and Dissertations

We develop two different descriptors which can be utilized to describe satellite imagery. The first, the differential-magnitude and radius descriptor, describes a scene by computing the directional gradient of the scene with respect to a vector field whose solutions are circles around a pixel to be described, and then counts pixels in a descriptor matrix according to the magnitude of this gradient and the distance at which this magnitude occurs. The second, the radial Fourier descriptor, extracts from the scene a sequence of annuloid sectors, and uses this to approximate the behavior of the image on a circle around the …

On Variable Bandwidth Kernel Density And Regression Estimation, Janet Nakarmi

Electronic Theses and Dissertations

We study the ideal variable bandwidth kernel density estimator introduced by McKay (1993) and the plug-in practical version of the variable bandwidth kernel density estimator with two sequences of bandwidths as in Ginè and Sang (2013).We estimate the variance of the variable bandwidth kernel density estimator. Based on the exact formula of the bias and the variance of the variable bandwidth kernel density estimator, we develop the optimal bandwidth selection of the true variable bandwidth kernel density estimator. Furthermore, we present the central limit theorem of the true variable bandwidth kernel density estimator. We also propose a new variable bandwidth …

Garch(1,1) With Sifted Gamma-Distributed Errors, Alan C. Budd

Electronic Theses and Dissertations

Typical General Autoregressive Conditional Heteroskedastic (GARCH) processes involve normally-distributed errors, and they model strictly-positive error processes poorly. This thesis will present a method for estimating the parameters of a GARCH(1,1) process with shifted Gamma-distributed errors, conduct a simulation study to test the method, and apply the method to real time series data.