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Articles 1 - 22 of 22
Full-Text Articles in Mathematics
Evaluating Variance Of The Model Credibility Index, Yan Xiao
Evaluating Variance Of The Model Credibility Index, Yan Xiao
Mathematics Theses
Model credibility index is defined to be a sample size under which the power of rejection equals 0.5. It applies goodness-of-fit testing thinking and uses a one-number summary statistic as an assessment tool in a false model world. The estimation of the model credibility index involves a bootstrap resampling technique. To assess the consistency of the estimator of model credibility index, we instead study the variance of the power achieved at a fixed sample size. An improved subsampling method is proposed to obtain an unbiased estimator of the variance of power. We present two examples to interpret the mechanics of …
Selecting The Working Correlation Structure By A New Generalized Aic Index For Longitudinal Data, Wei-Lun Lin
Selecting The Working Correlation Structure By A New Generalized Aic Index For Longitudinal Data, Wei-Lun Lin
Mathematics Theses
The analysis of longitudinal data has been a popular subject for the recent years. The growth of the Generalized Estimating Equation (GEE) Liang & Zeger, 1986) is one of the most influential recent developments in statistical practice for this practice. GEE methods are attractive both from a theoretical and a practical standpoint. In this paper, we are interested in the influence of different "working" correlation structures for modeling the longitudinal data. Furthermore, we propose a new AIC-like method for the model assessment which generalized AIC from the point of view of the data generating. By comparing the difference of the …
The Exponential Function Of Matrices, Nathalie Nicholle Smalls
The Exponential Function Of Matrices, Nathalie Nicholle Smalls
Mathematics Theses
The matrix exponential is a very important subclass of functions of matrices that has been studied extensively in the last 50 years. In this thesis, we discuss some of the more common matrix functions and their general properties, and we specifically explore the matrix exponential. In principle, the matrix exponential could be computed in many ways. In practice, some of the methods are preferable to others, but none are completely satisfactory. Computations of the matrix exponential using Taylor Series, Scaling and Squaring, Eigenvectors, and the Schur Decomposition methods are provided.
Empirical Likelihood Based Confidence Intervals For The Difference Between Two Sensitivities Of Continuous-Scale Diagnostic Tests At A Fixed Level Of Specificity, Suqin Yao
Mathematics Theses
Diagnostic testing is essential to distinguish non-diseased individuals from diseased individuals. The sensitivity and specificity are two important indices for the diagnostic accuracy of continuous-scale diagnostic tests. If we want to compare the effectiveness of two tests, it is of interest to construct a confidence interval for the difference of the two sensitivities at a fixed level of specificity. In this thesis, we propose two empirical likelihood based confidence intervals (HBELI and HBELII) for the difference of two sensitivities at a predetermined specificity level. Simulation studies show that when correlation between the two test results exists, HBELI and HBELII intervals …
Empirical Likelihood Confidence Intervals For Generalized Lorenz Curve, Nelly E. Belinga-Hill
Empirical Likelihood Confidence Intervals For Generalized Lorenz Curve, Nelly E. Belinga-Hill
Mathematics Theses
Lorenz curves are extensively used in economics to analyze income inequality metrics. In this thesis, we discuss confidence interval estimation methods for generalized Lorenz curve. We first obtain normal approximation (NA) and empirical likelihood (EL) based confidence intervals for generalized Lorenz curves. Then we perform simulation studies to compare coverage probabilities and lengths of the proposed EL-based confidence interval with the NA-based confidence interval for generalized Lorenz curve. Simulation results show that the EL-based confidence intervals have better coverage probabilities and shorter lengths than the NA-based intervals at 100p-th percentiles when p is greater than 0.50. Finally, two real examples …
Inference For Cox's Regression Model Via A New Version Of Empirical Likelihood, Ali Jinnah
Inference For Cox's Regression Model Via A New Version Of Empirical Likelihood, Ali Jinnah
Mathematics Theses
Cox Proportional Hazard Model is one of the most popular tools used in the study of Survival Analysis. Empirical Likelihood (EL) method has been used to study the Cox Proportional Hazard Model. In recent work by Qin and Jing (2001), empirical likelihood based confidence region is constructed with the assumption that the baseline hazard function is known. However, in Cox’s regression model the baseline hazard function is unspecified. In this thesis, we re-formulate empirical likelihood for the vector of regression parameters by estimating the baseline hazard function. The EL confidence regions are obtained accordingly. In addition, Adjusted Empirical Likelihood (AEL) …
Individual Growth Models Of Change In Peabody Picture Vocabulary Scores Of Children Treated For Brain Tumors, Ying Shen
Mathematics Theses
The individual growth model is a relatively new statistical technique. It is now widely used to examine the trajectories of individuals and groups in repeated measures data. This study examines the association of the receptive vocabulary over time and characteristics of children who were treated for brain tumors. The children undertook different types of treatment from one to any combinations of surgery, radiation and chemotherapy. The individual growth model is used to analyze the longitudinal data and to address the issues behind the data. Results of this study present several factors' influences to the rate of change of PPVT scores. …
An Optimal Solution On Screening And Treatment Of Chlamydia Trachomatis And Neisseria Gonorrhoeae, Xin Wei
An Optimal Solution On Screening And Treatment Of Chlamydia Trachomatis And Neisseria Gonorrhoeae, Xin Wei
Mathematics Theses
We propose a resource allocation model for the management of the fund for the screening and treatment of women infected by Chlamydia trachomatis and Neisseria gonorrhoeae. The goal is to maximize the number of infected women cured of Chlamydia trachomatis and Neisseria gonorrhoeae infections. The population going for screening is divided into groups by ages and races. The group number is dynamic. Dierent groups have dierent infection rates. There are four possible test assays and four possible treatments. We employed a two-phase algorithm to solve the problem. The first phase is small so an exhaustive method is applied, while the …
Study Of Factors Of Affecting Recurrence Of Myoma After Myomectomy, Lu Wang
Study Of Factors Of Affecting Recurrence Of Myoma After Myomectomy, Lu Wang
Mathematics Theses
This study is performed to evaluate the factors associated with the recurrence of myoma after Myomectomy. Identifying the factors of myoma recurrence will assist the patient and her gynecologist in deciding the most appropriate method of treatment according to her specific social, medical and emotional needs. Multiple logistic regression is used to determine the factors affecting the recurrence. 'Age of Surgery', 'Tumor Size', 'Pelvic Pain' and the interaction between the 'Age of Surgery' and 'Tumor Size' are significant in the final model. Kaplan-Meier method is used to calculate the cumulative recurrence rate. The 5 year cumulative recurrence rate is 24.32% …
Polynomial Functions Over Rings Of Residue Classes Of Integers, M Brandon Meredith
Polynomial Functions Over Rings Of Residue Classes Of Integers, M Brandon Meredith
Mathematics Theses
In this thesis we discuss how to find equivalent representations of polynomial functions over the ring of integers modulo a power of a prime. Specifically, we look for lower degree representations and representations with fewer variables for which important applications in electrical and computer engineering exist. We present several algorithms for finding these compact formulations.
Empirical Likelihood-Based Nonparametric Inference For The Difference Between Two Partial Aucs, Yan Yuan
Empirical Likelihood-Based Nonparametric Inference For The Difference Between Two Partial Aucs, Yan Yuan
Mathematics Theses
Compare the accuracy of two continuous-scale tests is increasing important when a new test is developed. The traditional approach that compares the entire areas under two Receiver Operating Characteristic (ROC) curves is not sensitive when two ROC curves cross each other. A better approach to compare the accuracy of two diagnostic tests is to compare the areas under two ROC curves (AUCs) in the interested specificity interval. In this thesis, we have proposed bootstrap and empirical likelihood (EL) approach for inference of the difference between two partial AUCs. The empirical likelihood ratio for the difference between two partial AUCs is …
Empirical Likelihood Confidence Intervals For The Sensitivity Of A Continuous-Scale Diagnostic Test, Angela Elaine Davis
Empirical Likelihood Confidence Intervals For The Sensitivity Of A Continuous-Scale Diagnostic Test, Angela Elaine Davis
Mathematics Theses
Diagnostic testing is essential to distinguish non-diseased individuals from diseased individuals. More accurate tests lead to improved treatment and thus reduce medical mistakes. The sensitivity and specificity are two important measurements for the diagnostic accuracy of a diagnostic test. When the test results are continuous, it is of interest to construct a confidence interval for the sensitivity at a fixed level of specificity for the test. In this thesis, we propose three empirical likelihood intervals for the sensitivity. Simulation studies are conducted to compare the empirical likelihood based confidence intervals with the existing normal approximation based confidence interval. Our studies …
An Extension Of Ramsey's Theorem To Multipartite Graphs, Brian Michael Cook
An Extension Of Ramsey's Theorem To Multipartite Graphs, Brian Michael Cook
Mathematics Theses
Ramsey Theorem, in the most simple form, states that if we are given a positive integer l, there exists a minimal integer r(l), called the Ramsey number, such any partition of the edges of K_r(l) into two sets, i.e. a 2-coloring, yields a copy of K_l contained entirely in one of the partitioned sets, i.e. a monochromatic copy of Kl. We prove an extension of Ramsey's Theorem, in the more general form, by replacing complete graphs by multipartite graphs in both senses, as the partitioned set and as the desired monochromatic graph. More formally, given integers l and k, there …
Bayesian Approach To Three-Arm Non Inferiority Trials, Marcus Chenier Britton
Bayesian Approach To Three-Arm Non Inferiority Trials, Marcus Chenier Britton
Mathematics Theses
In non-inferiority trials, the goal is to show how an experimental treatment is statistically and clinically not inferior to the active control. The three-arm clinical trial usually recommended for non-inferiority trials by the FDA. The three-arm trial consists of a placebo, reference, and an experimental treatment. The three-arm trial shows the superiority of the reference over the placebo and comparison of the reference to an experimental treatment. In this paper, I will assess a non-inferiority trial with Bayesian methods. By employing Bayesian analysis, the parameters are random and assign vague prior distributions. I will compare the models involving different prior …
Omnibus Tests For Comparison Of Competing Risks With Covariate Effects Via Additive Risk Model, Duytrac Vu Nguyen
Omnibus Tests For Comparison Of Competing Risks With Covariate Effects Via Additive Risk Model, Duytrac Vu Nguyen
Mathematics Theses
It is of interest that researchers study competing risks in which subjects may fail from any one of K causes. Comparing any two competing risks with covariate effects is very important in medical studies. This thesis develops omnibus tests for comparing cause-specific hazard rates and cumulative incidence functions at specified covariate levels. In the thesis, the omnibus tests are derived under the additive risk model, that is an alternative to the proportional hazard model, with by a weighted difference of estimates of cumulative cause-specific hazard rates. Simultaneous confidence bands for the difference of two conditional cumulative incidence functions are also …
Spectrally Arbitrary And Inertially Arbitrary Sign Pattern Matrices, Nilay Sezin Demir
Spectrally Arbitrary And Inertially Arbitrary Sign Pattern Matrices, Nilay Sezin Demir
Mathematics Theses
A sign pattern(matrix) is a matrix whose entries are from the set {+,-,0}. An n x n sign pattern matrix is a spectrally arbitrary pattern(SAP) if for every monic real polynomial p(x) of degree n, there exists a real matrix B whose entries agree in sign with A such that the characteristic polynomial of B is p(x). An n x n pattern A is an inertialy arbitrary pattern(IAP) if (r,s,t) belongs to the inertia set of A for every nonnegative triple (r,s,t) with r+s+t=n. Some elementary results on these two classes of patterns are first exhibited. Tree sign patterns are …
Analyzing The Behavior Of Rats By Repeated Measurements, Kenita A. Hall
Analyzing The Behavior Of Rats By Repeated Measurements, Kenita A. Hall
Mathematics Theses
Longitudinal data, which is also known as repeated measures, has grown increasingly within the past years because of its ability to monitor change both within and between subjects. Statisticians in many fields of study have chosen this way of collecting data because it is cost effective and it minimizes the number of subjects required to produce a meaningful outcome. This thesis will explore the world of longitudinal studies to gain a thorough understanding of why this type of collecting data has grown so rapidly. This study will also describe several methods to analyze repeated measures using data collected on the …
Forecasting The Chinese Futures Markets Prices Of Soy Bean And Green Bean Commodities, Kouadio Kouman Dongo
Forecasting The Chinese Futures Markets Prices Of Soy Bean And Green Bean Commodities, Kouadio Kouman Dongo
Mathematics Theses
Using both single and vector processes, we fitted the Box-Jenkin’s ARIMA model and the Vector Autoregressive model following the Johansen approach, to forecast soy bean and green bean prices on the Chinese futures markets. The results are encouraging and provide empirical evidence that the vector processes perform better than the single series. The co-integration test indicated that the null hypothesis of no co-integration among the relevant variables could be rejected. This is one of the most important findings in this paper. The purposes for analyzing and modeling the series jointly are to understand the dynamic relationships over time among the …
The Square Root Function Of A Matrix, Crystal Monterz Gordon
The Square Root Function Of A Matrix, Crystal Monterz Gordon
Mathematics Theses
Having origins in the increasingly popular Matrix Theory, the square root function of a matrix has received notable attention in recent years. In this thesis, we discuss some of the more common matrix functions and their general properties, but we specifically explore the square root function of a matrix and the most efficient method (Schur decomposition) of computing it. Calculating the square root of a 2×2 matrix by the Cayley-Hamilton Theorem is highlighted, along with square roots of positive semidefinite matrices and general square roots using the Jordan Canonical Form.
Longitudinal Curves For Behaviors Of Children Diagnosed With A Brain Tumor, Huayan Chai
Longitudinal Curves For Behaviors Of Children Diagnosed With A Brain Tumor, Huayan Chai
Mathematics Theses
Change in adaptive outcomes of children who are treated for brain tumors is examined using longitudinal data. The children received different types of treatment from none to any combinations of three treatments, which are surgery, radiation and chemotherapy. In this thesis, we use mixed model to find the significant variables that predict change in outcomes of communication skill, daily living skills and socialization skill. Fractional polynomial transformation method and Gompertz method are applied to build non-linear longitudinal curves. We use PRESS as the criterion to compare these two methods. Comparison analysis shows the effect of each significant variable on adaptive …
Critical Mathematics Pedagogy: Transforming Teachers’ Practices, David W. Stinson, Carla R. Bidwell, Christopher C. Jett, Ginny C. Powell, Mary M. Thurman
Critical Mathematics Pedagogy: Transforming Teachers’ Practices, David W. Stinson, Carla R. Bidwell, Christopher C. Jett, Ginny C. Powell, Mary M. Thurman
Middle-Secondary Education and Instructional Technology Faculty Publications
This study reports the effects of a graduate-level mathematics education course that focused on critical theory and teaching for social justice on the pedagogical philosophies and practices of three mathematics teachers (middle, high school, and 2-year college). The study employed Freirian participatory research methodology; in fact, the participants were not only co-researchers, but also co-authors of the study. Data collection included reflective essays, journals, and “storytelling”; data analysis was a combination of textual analysis and autoethnography. The findings report that the teachers believed that the course provided not only a new language but also a legitimization to transform their pedagogical …
What Is Mathematics?: Teachers Exploring The Philosophy Of Mathematics, Kimberly White-Fredette, David W. Stinson
What Is Mathematics?: Teachers Exploring The Philosophy Of Mathematics, Kimberly White-Fredette, David W. Stinson
Middle-Secondary Education and Instructional Technology Faculty Publications
No abstract provided.