Statistics and Probability Commons^™

Evaluation Of Area Under The Constant Shape Bi-Weibull Roc Curve, Sudesh Pundir, R Amala

Journal of Modern Applied Statistical Methods

The Receiver Operating Characteristic (ROC) curve generated based on assuming a constant shape Bi-Weibull distribution is studied. In the context of ROC curve analysis, it is assumed that biomarker values from controls and cases follow some specific distribution and the accuracy is evaluated by using the ROC model developed from that specified distribution. This article assumes that the biomarker values from the two groups follow Weibull distributions with equal shape parameter and different scale parameters. The ROC model, area under the ROC curve (AUC), asymptotic and bootstrap confidence intervals for the AUC are derived. Theoretical results are validated by simulation …

Investigating The Feasibility Of Using Mplus In The Estimation Of Growth Mixture Models, Ming Li, Jeffrey R. Harring, George B. Macready

Journal of Modern Applied Statistical Methods

Hipp and Bauer (2006) investigated the issues of singularities and local maximum solutions within growth mixture models (GMMs) and made recommendations regarding the use of multiple starting values. Building on their work, this simulation study investigates the feasibility of estimating GMMs within Mplus as measured by convergence to proper, but local solutions.

Unifying Specific Climate Research With A Molar Climate Measure: A Situational Affordances Approach, Alice Brawley

All Theses

Organizational climate - briefly, the shared perceptions of a workplace - was originally studied as a molar concept, but this approach generally lacked focus and thus resulted in unmanageable measures. Organizational climate research has been subdivided into many areas of specific climate research focusing on particular organizational factors or outcomes, such as safety or customer service (Schneider, Ehrhart, & Macey, 2013). While the study of specific climates has been and remains worthwhile, recent literature in the area has called for a return to the molar or global conceptualization of organizational climate (Kuenzi & Schminke, 2009; Schneider et al., 2013). In …

Poisson Distributed Individuals Control Charts With Optimal Limits, Negin Enayaty Ahangar

Graduate Theses and Dissertations

The conventional method used in attribute control charts is the Shewhart three sigma limits. The implicit assumption of the Normal distribution in this approach is not appropriate for skewed distributions such as Poisson, Geometric and Negative Binomial. Normal approximations perform poorly in the tail area of the these distributions. In this research, a type of attribute control chart is introduced to monitor the processes that provide count data. The economic objective of this chart is to minimize the cost of its errors which is determined by the designer. This objective is a linear function of type I and II errors. …

A Reduced Bias Method Of Estimating Variance Components In Generalized Linear Mixed Models, Elizabeth A. Claassen

Department of Statistics: Dissertations, Theses, and Student Research

In small samples it is well known that the standard methods for estimating variance components in a generalized linear mixed model (GLMM), pseudo-likelihood and maximum likelihood, yield estimates that are biased downward. An important consequence of this is that inferences on fixed effects will have inflated Type I error rates because their precision is overstated. We introduce a new method for estimating parameters in GLMMs that applies a Firth bias adjustment to the maximum likelihood-based GLMM estimating algorithm. We apply this technique to one- and two-treatment logistic regression models with a single random effect. We show simulation results that demonstrate …

A Stochastic Parameter Regression Model For Long Memory Time Series, Rose Marie Ocker

Boise State University Theses and Dissertations

In a complex and dynamic world, the assumption that relationships in a system remain constant is not necessarily a well-founded one. Allowing for time-varying parameters in a regression model has become a popular technique, but the best way to estimate the parameters of the time-varying model is still in discussion. These parameters can be autocorrelated with their past for a long time (long memory), but most of the existing models for parameters are of the short memory type, leaving the error process to account for any long memory behavior in the response variable. As an alternative, we propose a long …

Table Games Revenue Management: A Bayesian Approach, Daryl F. Boykin

UNLV Theses, Dissertations, Professional Papers, and Capstones

With growing competition for casino floor space, the Table Games department is under increased pressure to improve revenues. Current systems in the department rely upon a supervisor's intuitive knowledge about business trends hourly to respond to business levels. By using Bayesian analysis, it is possible to develop a functional revenue management system for making optimal business decisions in the Table Game Departments.

High Frequency Data: Modeling Durations Via The Acd And Log Acd Models, Lilian Cheung

Honors Scholar Theses

This thesis proposes a method of finding initial parameter estimates in the Log ACD₁ model for use in recursive estimation. The recursive estimating equations method is applied to the Log ACD₁ model to find recursive estimates for the unknown parameters in the model. A literature review is provided on the ACD and Log ACD models, and on the theory of estimating equations. Monte Carlo simulations indicate that the proposed method of finding initial parameter estimates is viable. The parameter estimation process is demonstrated by fitting an ACD model and a Log ACD model to a set of IBM …

Comparison Of Different Methods For Estimating Log-Normal Means, Qi Tang

Electronic Theses and Dissertations

The log-normal distribution is a popular model in many areas, especially in biostatistics and survival analysis where the data tend to be right skewed. In our research, a total of ten different estimators of log-normal means are compared theoretically. Simulations are done using different values of parameters and sample size. As a result of comparison, ``A degree of freedom adjusted" maximum likelihood estimator and Bayesian estimator under quadratic loss are the best when using the mean square error (MSE) as a criterion. The ten estimators are applied to a real dataset, an environmental study from Naval Construction Battalion Center (NCBC), …

Time Series Decomposition Using Singular Spectrum Analysis, Cheng Deng

Electronic Theses and Dissertations

Singular Spectrum Analysis (SSA) is a method for decomposing and forecasting time series that recently has had major developments but it is not yet routinely included in introductory time series courses. An international conference on the topic was held in Beijing in 2012. The basic SSA method decomposes a time series into trend, seasonal component and noise. However there are other more advanced extensions and applications of the method such as change-point detection or the treatment of multivariate time series. The purpose of this work is to understand the basic SSA method through its application to the monthly average sea …

Are Highly Dispersed Variables More Extreme? The Case Of Distributions With Compact Support, Benedict E. Adjogah

Electronic Theses and Dissertations

We consider discrete and continuous symmetric random variables X taking values in [0; 1], and thus having expected value 1/2. The main thrust of this investigation is to study the correlation between the variance, Var(X) of X and the value of the expected maximum E(Mn) = E(X1,...,Xn) of n independent and identically distributed random variables X1,X2,...,Xn, each distributed as X. Many special cases are studied, some leading to very interesting alternating sums, and some progress is made towards a general theory.

The Association Between The Il-1 Pathway, Isaac C. Wun

Dissertations and Theses (Open Access)

Cutaneous malignant melanoma (CMM) is a potentially lethal malignancy that warrants attention and further research, as it is known to that there is an increasing rate of incidence in theUnited States, and it is also known that exposure to UV light is its most crucial risk factor, and family history of melanoma is also an important risk factor. Melanoma is an aggressive and lethal cancer in humans. There are an estimated new 132,000 melanoma cases annually worldwide, and the trend has doubled in the past 20 years. However, attempts to treat melanoma have encountered considerable resistance and remained ineffective. The …

Implementation And Application Of The Curds And Whey Algorithm To Regression Problems, John Kidd

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A common statistical problem is trying to predict two or more variables using a set of predictor variables. The simplest model for this situation is called multivariate linear regression. This method uses each set of predictor variables to predict each of the response variables separately. This approach seems counter-intuitive as any possible relationship between the variables being predicted is ignored.

Breiman and Friedman found a way to take advantage of relationships among the response variables to increase the accuracy of the predictions for each of the predicted variables with an algorithm they called Curds and
Whey. It uses other statistical …

Computational Topics In Lie Theory And Representation Theory, Thomas J. Apedaile

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The computer algebra system Maple contains a basic set of commands for working with Lie algebras and matrices. The purpose of this thesis was to extend the functionality of these Maple packages in a number of important areas. First, programs for defining multiplication in several different types of algebras were created to allow users to perform a wider variety of calculations. Second, commands were created for calculating some basic properties of matrix representations of semisimple Lie algebras. This allows a user to identify a given matrix representation by a collection of integers which do not change when the basis of …

Physically Based Preconditioning Techniques Applied To The First Order Particle Transport And To Fluid Transport In Porous Media, Michael Rigley

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Solving linear systems is at the heart of many scientific applications from the PreAlgebra's student solving for x and y for basic geometry problems to the computational scientist solving billions of equations with billions of variables for weather forecasting, modeling fusion reactions, or web search algorithms. In this study we look at improving the efficiency of solving large linear systems that result from two applications. The first includes linear systems that result from solving differential equations for the movement of atomic particles in particle emitting, void, and absorbing regions. The second includes solving linear systems that result from solving differential …

Family-Wise Error Rate Control In Quantitative Trait Loci (Qtl) Mapping And Gene Ontology Graphs With Remarks On Family Selection, Garrett Saunders

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

One of the great aims of statistics, the science of collecting, analyzing, and interpreting data, is to protect against the probability of falsely rejecting an accepted claim, or hypothesis, given observed data stemming from some experiment. This is generally known as protecting against a Type I Error, or controlling the Type I Error rate. The extension of this protection against Type I Errors to the situation where thousands upon thousands of hypothesis are examined simultaneously is known as multiple hypothesis testing. This dissertation presents an improvement to an existing multiple hypothesis testing approach, the Focus Level method, specific to gene …

Beetles, Fungi And Trees: A Story For The Ages? Modeling And Projecting The Multipartite Symbiosis Between The Mountain Pine Beetle, Dendroctonus Ponderosae, And Its Fungal Symbionts, Grosmannia Clavigera And Ophiostoma Montium, Audrey L. Addison

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

As data collection and modeling improve, ecologists increasingly discover that interspecies dynamics greatly affect the success of individual species. Models accounting for the dynamics of multiple species are becoming more important. In this work, we explore the relationship between mountain pine beetle (MPB, Dendroctonus ponderosae Hopkins) and two mutualistic fungi, Grosmannia clavigera and Ophiostoma montium. These species are involved in a multipartite symbiosis, critical to the survival of MPB, in which each species benefits.

Extensive phenological modeling has been done to determine how temperature affects the timing of life events and cold-weather mortality of MPB. The fungi have also …

Statistical Modeling, Exploration, And Visualization Of Snow Water Equivalent Data, James Beguah Odei

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Due to a continual increase in the demand for water as well as an ongoing regional drought, there is an imminent need to monitor and forecast water resources in the Western United States. In particular, water resources in the Intermountain West rely heavily on snow water storage. Thus, the need to improve seasonal forecasts of snowpack and considering new techniques would allow water resources to be more effectively managed throughout the entire water-year. Many available models used in forecasting snow water equivalent (SWE) measurements require delicate calibrations.

In contrast to the physical SWE models most commonly used for forecasting, we …

Patient Rule Induction Method For Subgroup Identification Given Censored Data., Patrick James Trainor

Electronic Theses and Dissertations

The identification of subgroups in clinical studies is an important aspect of personalized medicine. In order to develop tailored therapeutics, the factors that characterize subgroups with differential prognosis, response to treatment, and incidence of adverse events or toxicities must be elucidated. We present a generalization of a statistical learning algorithm, Patient Rule Induction Method (PRIM), that is well suited for this task given a right-censored time-to-event outcome measure. This algorithm works to recursively partition a covariate space into mutually exclusive boxes that can be utilized to define subgroups. Conceptually the algorithm is similar to classification and regression trees but rather …

Family-Wise Error Rate Control In Quantitative Trait Loci (Qtl) Mapping And Gene Ontology Graphs With Remarks On Family Selection, Garrett Saunders

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

One of the great aims of statistics, the science of collecting, analyzing, and interpreting data, is to protect against the probability of falsely rejecting an accepted claim, or hypothesis, given observed data stemming from some experiment. This is generally known as protecting against a Type I Error, or controlling the Type I Error rate. The extension of this protection against Type I Errors to the situation where thousands upon thousands of hypotheses are examined simultaneously is known as multiple hypothesis testing. This dissertation presents an improvement to an existing multiple hypothesis testing approach, the Focus Level method, specific to gene …