Statistics and Probability Commons^™

A Comparative Study For Bandwidth Selection In Kernel Density Estimation, Omar M. Eidous, Mohammad Abd Alrahem Shafeq Marie, Mohammed H. Baker Al-Haj Ebrahem

Journal of Modern Applied Statistical Methods

Nonparametric kernel density estimation method does not make any assumptions regarding the functional form of curves of interest; hence it allows flexible modeling of data. A crucial problem in kernel density estimation method is how to determine the bandwidth (smoothing) parameter. This article examines the most important bandwidth selection methods, in particular, least squares cross-validation, biased crossvalidation, direct plug-in, solve-the-equation rules and contrast methods. Methods are described and expressions are presented. The main practical contribution is a comparative simulation study that aims to isolate the most promising methods. The performance of each method is evaluated on the basis of the …

Survival Prediction For Brain Tumor Patients Using Gene Expression Data, Vinicius Bonato

Dissertations and Theses (Open Access)

Brain tumor is one of the most aggressive types of cancer in humans, with an estimated median survival time of 12 months and only 4% of the patients surviving more than 5 years after disease diagnosis. Until recently, brain tumor prognosis has been based only on clinical information such as tumor grade and patient age, but there are reports indicating that molecular profiling of gliomas can reveal subgroups of patients with distinct survival rates. We hypothesize that coupling molecular profiling of brain tumors with clinical information might improve predictions of patient survival time and, consequently, better guide future treatment decisions. …

General Coupon Collecting Models And Multinomial Games, James Y. Lee

UNLV Theses, Dissertations, Professional Papers, and Capstones

The coupon collection problem is one of the most studied problems in statistics. It is the problem of collecting r (r<∞) distinct coupons one by one from k different kinds (k<∞) of coupons. We note that this is equivalent to the classical occupancy problem which involves the random allocation of r distinct balls into k distinct cells. Although the problem was first introduced centuries ago, it is still actively investigated today. Perhaps its greatest feature is its versatility, numerous approaches, and countless variations. For this reason, we are particularly interested in creating a classification system for the many generalizations of the coupon collection problem. In this thesis, we will introduce models that will be able to categorize these generalizations. In addition, we calculate the waiting time for the models under consideration. Our approach is to use the Dirichlet Type II integral. We compare our calculations to the ones obtained through Monte Carlo simulation. Our results will show that our models and the method used to find the waiting times are ideal for solving problems of this type.

Factors Affecting Reading Outcomes Across Time In Bureau Of Indian Education Reading First Schools, Heather J. Chapman

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Regardless of age, background, or socioeconomic status, children must learn to read in order to be successful in school and in their future careers. Reading is an essential skill necessary to be successful in all other academic content areas. Despite the importance of this skill, American Indian children consistently score below the national average on tests of reading ability and reading comprehension. During recent years, many schools in the Bureau of Indian Education (BIE) system requested funding through the Reading First initiative. Schools used the funding and support provided by the BIE Reading First grant to attempt system-wide change at …

Three Essays On Environmental- And Spatial-Based Valuation Of Urban Land And Housing, Lu Liu

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This dissertation attempts to provide a comprehensive examination on the non-market valuation of the effect of open space amenities and local public infrastructure on the value of urban land and housing with both spatial heterogeneity and project heterogeneity. The demand for raw land is a derived demand for housing built on it. Therefore, we need to examine the land market and the housing market together. On the one hand, we estimate the value of urban land in a market that does not satisfy the usual assumptions of a competitive market structure as well as incentive incompatibility issues for transaction participants, …

Goodness-Of-Fit And Change-Point Tests For Functional Data, Robertas Gabrys

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A test for independence and identical distribution of functional observations is proposed in this thesis. To reduce dimension, curves are projected on the most important functional principal components. Then a test statistic based on lagged cross--covariances of the resulting vectors is constructed. We show that this dimension reduction step introduces asymptotically negligible terms, i.e. the projections behave asymptotically as iid vector--valued observations. A complete asymptotic theory based on correlations of random matrices, functional principal component expansions, and Hilbert space techniques is developed. The test statistic has X²-square asymptotic null distribution.

Two inferential tests for error correlation in the …

On Robustification Of Some Procedures Used In Analysis Of Covariance, Kuanwong Watcharotone

Dissertations

This study discusses robust procedures for the analysis of covariance (ANCOVA) models. These methods are based on rank-based (R) fitting procedures, which are quite analogous to the traditional ANCOVA methods based on least squares fits. Our initial empirical results show that the validity of R procedures is similar to the least squares procedures. In terms of power, there is a small loss in efficiency to least squares methods when the random errors have a normal distribution but the rank-based procedures are much more powerful for the heavy-tailed error distributions in our study.

Rank-based analogs are also developed for pick-a-point, adjusted …

Pre-Service Teachers’ Knowledge Of Algebraic Thinking And The Characteristics Of The Questions Posed For Students, Leigh A. Van Den Kieboom, Marta Magiera, John Moyer

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this study, we explored the relationship between the strength of pre-service teachers’ algebraic thinking and the characteristics of the questions they posed during cognitive interviews that focused on probing the algebraic thinking of middle school students. We developed a performance rubric to evaluate the strength of pre-service teachers’ algebraic thinking across 130 algebra-based tasks. We used an existing coding scheme found in the literature to analyze the characteristics of the questions pre-service teachers posed during clinical interviews. We found that pre-service teachers with higher algebraic thinking abilities were able to pose probing questions that uncovered student thinking through the …

Pre-Service Middle School Teachers’ Knowledge Of Algebraic Thinking, Marta Magiera, John Moyer, Leigh A. Van Den Kieboom

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this study we examined the relationship between 18 pre-service middle school teachers’ own ability to use algebraic thinking to solve problems and their ability to recognize and interpret the algebraic thinking of middle school students. We assessed the pre-service teachers’ own algebraic thinking by examining their solutions and explanations to multiple algebra-based tasks posed during a semester-long mathematics content course. We assessed their ability to recognize and interpret the algebraic thinking of students in two ways. The first was by analyzing the preservice teachers’ ability to interpret students’ written solutions to open-ended algebra-based tasks. The second was by analyzing …

A Numerical Method For Estimating The Variance Of Age At Maximum Growth Rate In Growth Models, Semhar Ogbagaber

Theses and Dissertations

Most studies on maturation and body composition using the Fels Longitudinal data mention peak height velocity (PHV) as an important outcome measure. The PHV is often derived from growth models such as the triple logistic model fitted to the stature (height) data. The age at PHV is sometimes ordinalized to designate an individual as an early, average or late maturer. In theory, age at PHV is the age at which the rate of growth reaches the maximum. Theoretically, for a well behaved growth function, this could be obtained by setting the second derivative of the growth function to zero and …

Multiple Regression Analysis: Sfa Professors' Salaries, Latonya Edmeade

Undergraduate Research Conference

There is always a certain curiosity and controversy surrounding professor’s salaries and whether they are overpaid or not paid enough. We have decided to try and untangle this wonder by creating a regression model in which the average person could easily understand while solving this lingering question. It is the average student’s opinion that professors make way too much compared to their daily tasks.

On the other hand, many professors are always complaining that they are not paid enough with their advanced degree and work load, not to mention the option always hovers over their head of pursuing a different …

War By Government: Which Systems Are Most Likely To Engage In Conflict?, Courtney Lemon

Undergraduate Research Conference

No abstract provided.

Default Rate On Auto Loans, Jessica Jones

Undergraduate Research Conference

In completing this model, we want to view a portfolio of loans at a bank and be able to predict the default rate on an auto loan. We also want to be able to look at an individual loan and predict the default probability taking into consideration interest rate, term, number of days late, times late, original loan amount, collateral value, LTV and credit score. The data will assist in forecasting default rates in future years and in projecting income and loss for a bank. We predict at the end of the model, credit score will be the main indicator …

Nonparametric Regression With Missing Outcomes Using Weighted Kernel Estimating Equations, Lu Wang, Andrea Rotnitzky, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

Nonparametric And Semiparametric Analysis Of Current Status Data Subject To Outcome Misclassification, Victor G. Sal Y Rosas, James P. Hughes

UW Biostatistics Working Paper Series

In this article, we present nonparametric and semiparametric methods to analyze current status data subject to outcome misclassification. Our methods use nonparametric maximum likelihood estimation (NPMLE) to estimate the distribution function of the failure time when sensitivity and specificity may vary among subgroups. A nonparametric test is proposed for the two sample hypothesis testing. In regression analysis, we apply the Cox proportional hazard model and likelihood ratio based confidence intervals for the regression coefficients are proposed. Our methods are motivated and demonstrated by data collected from an infectious disease study in Seattle, WA.

Parameter Estimation In Linear-Linear Segmented Regression, Erika Lyn Hernandez

Theses and Dissertations

Segmented regression is a type of nonlinear regression that allows differing functional forms to be fit over different ranges of the explanatory variable. This paper considers the simple segmented regression case of two linear segments that are constrained to meet, often called the linear-linear model. Parameter estimation in the case where the joinpoint between the regimes is unknown can be tricky. Using a simulation study, four estimators for the parameters of the linear-linear model are evaluated. The bias and mean squared error of the estimators are considered under differing parameter combinations and sample sizes. Parameters estimated in the model are …

Cluster And Classification Analysis Of Fossil Invertebrates Within The Bird Spring Formation, Arrow Canyon, Nevada: Implications For Relative Rise And Fall Of Sea-Level, Scott L. Morris

Theses and Dissertations

Carbonate strata preserve indicators of local marine environments through time. Such indicators often include microfossils that have relatively unique conditions under which they can survive, including light, nutrients, salinity, and especially water temperature. As such, microfossils are environmental proxies. When these microfossils are preserved in the rock record, they constitute key components of depositional facies. Spence et al. (2004, 2007) has proposed several approaches for determining the facies of a given stratigraphic succession based upon these proxies. Cluster analysis can be used to determine microfossil groups that represent specific environmental conditions. Identifying which microfossil groups exist through time can indicate …

Utilizing The Integrated Difference Of Two Survival Functions To Quantify The Treatment Contrast For Designing, Monitoring And Analyzing A Comparative Clinical Study, Lihui Zhao, Lu Tian, Hajime Uno, Scott D. Solomon, Marc A. Pfeffer, J. S. Schindler, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Recovery Of The Baseline Incidence Density In Censored Time-To-Event Analysis, Mikel Aickin

COBRA Preprint Series

Abstract Time-to-event analyses are often concerned with the effects of explanatory factors on the underlying incidence density, but since there is no intrinsic interest in the form of the incidence density itself, a proportional hazards model is used. When part of the purpose of the analysis is to use actual cumulative incidence for simulation, or for providing informative visual displays of the results, an estimate of the baseline incidence density is required. The usual method for estimating the baseline hazards in Cox’s proportional hazards analysis yields values that are of little use, and furthermore no standard deviations of the estimates …

Determining The Success Of Ncaa Basketball Teams Through Team Characteristics, Raymond Witkos

Honors Projects in Mathematics

Every year much of the nation becomes engulfed in the NCAA basketball postseason tournament more affectionately known as “March Madness.” The tournament has received the name because of the ability for any team to win a single game and advance to the next round. The purpose of this study is to determine whether concrete statistical measures can be used to predict the final outcome of the tournament. The data collected in the study include 13 independent variables ranging from the 2003-2004 season up until the current 2009-2010 season. Different tests were run in an attempt to achieve the most accurate …

Predictive Modeling Of Alumni Donor Behavior, Lauren Prue

Honors Projects in Mathematics

In recent years, college and universities have relied increasingly upon the charitable contributions of its previous graduates; as the costs of tuition rise substantially, development offices are facing the challenge of creating annual fund campaigns that are minimally expensive while providing the maximum potential for return. This study addresses the available constituent database at one University in particular in an effort to identify what criteria are the strongest predictors of donor response at a small, private university located within New England. The analysis utilized predictive modeling and data-mining largely within the software program Rapid Insight to build several models in …

Section Abstracts: Statistics

Virginia Journal of Science

Abstracts of the Statistics Section for the 88th Annual Meeting of the Virginia Academy of Science, May 20-21, 2010, James Madison University, Harrisonburg, Virginia.

On Construction Of The Smallest One-Sided Confidence Interval For The Difference Of Two Proportions, Weizhen Wang

Mathematics and Statistics Faculty Publications

For my class of one-sided 1 - α confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the difference of two proportions of two independent binomial random variables, is constructed based on a direct analysis of coverage probability function. A special ordering on the confidence limit is developed and the corresponding smallest confidence interval is derived. This interval is then applied to identify the minimum effective dose (MED) for binary data in dose-response studies, and a multiple test procedure that controls the familywise error rate at …

Insights Into The Commons On Flickr, Jason Vaughan

Library Faculty Research

The Commons on Flickr, comprised of an international community of select libraries, museums, and archives, was a project initially launched in 2008 by the Library of Congress and Flickr. Primary goals of The Commons are to broaden exposure to rich cultural heritage photographs and to observe and participate in the communities of engagement and dialog enabled through The Commons. A survey was administered to all The Commons institutions during summer 2009, focusing on assessment of the overall satisfaction of current members and seeking additional details on participation goals, social interactions, staff time involvement, and general statistics. Members report a very …

Efficient Design And Inference For Multi-Stage Randomized Trials Of Individualized Treatment Policies, Ree Dawson, Philip W. Lavori

COBRA Preprint Series

Increased clinical interest in individualized ‘adaptive’ treatment policies has shifted the methodological focus for their development from the analysis of naturalistically observed strategies to experimental evaluation of a pre-selected set of strategies via multi-stage designs. Because multi-stage studies often avoid the ‘curse of dimensionality’ inherent in uncontrolled studies, and hence the need to parametrically smooth trial data, it is not surprising in this context to find direct connections among different methodological approaches. We show by asymptotic and algebraic proof that the maximum likelihood (ML) and optimal semi-parametric estimators of the mean of a treatment policy and its standard error are …

Importance Sampling For Dispersion-Managed Solitons, Elaine T. Spiller, Gino Biondini

Mathematics, Statistics and Computer Science Faculty Research and Publications

The dispersion-managed nonlinear Schrödinger (DMNLS) equation governs the long-term dynamics of systems which are subject to large and rapid dispersion variations. We present a method to study large, noise-induced amplitude and phase perturbations of dispersion-managed solitons. The method is based on the use of importance sampling to bias Monte Carlo simulations toward regions of state space where rare events of interest—large phase or amplitude variations—are most likely to occur. Implementing the method thus involves solving two separate problems: finding the most likely noise realizations that produce a small change in the soliton parameters, and finding the most likely way that …

Knowing When To Say When: An Expanded Description Of Stopping Problems And Their Solutions, Eric C. Bauer

Mathematics

No abstract provided.

Rao's Quadratic Entropy And Some New Applications, Yueqin Zhao

Mathematics & Statistics Theses & Dissertations

Many problems in statistical inference are formulated as testing the diversity of populations. The entropy functions measure the similarity of a distribution function to the uniform distribution and hence can be used as a measure of diversity. Rao (1982a) proposed the concept of quadratic entropy. Its concavity property makes the decomposition similar to ANOVA for categorical data feasible. In this thesis, after reviewing the properties and providing a modification to quadratic entropy, various applications of quadratic entropy are explored. First, analysis of quadratic entropy with the suggested modification to analyze the contingency table data is explored. Then its application to …

Simple Examples Of Estimating Causal Effects Using Targeted Maximum Likelihood Estimation, Michael Rosenblum, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We present a brief overview of targeted maximum likelihood for estimating the causal effect of a single time point treatment and of a two time point treatment. We focus on simple examples demonstrating how to apply the methodology developed in (van der Laan and Rubin, 2006; Moore and van der Laan, 2007; van der Laan, 2010a,b). We include R code for the single time point case.

Can Animal Models Of Disease Reliably Inform Human Studies?, H. Bart Van Der Worp, David W. Howells, Emily Sena, Michelle J. Porritt, Sarah Rewell, Victoria O'Collins, Malcolm Macleod

Validation of Animal Experimentation Collection

• The value of animal experiments for predicting the effectiveness of treatment strategies in clinical trials has remained controversial, mainly because of a recurrent failure of interventions apparently promising in animal models to translate to the clinic.
• Translational failure may be explained in part by methodological flaws in animal studies, leading to systematic bias and thereby to inadequate data and incorrect conclusions about efficacy.
• Failures also result because of critical disparities, usually disease specific, between the animal models and the clinical trials testing the treatment strategy.
• Systematic review and meta-analysis of animal studies may aid in the selection of the most …