Statistics and Probability Commons^™

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 …

Publication Bias In Reports Of Animal Stroke Studies Leads To Major Overstatement Of Efficacy, Emily Sena, H. Bart Van Der Worp, Philip M.W. Bath, David W. Howells, Malcolm Macleod

Validation of Animal Experimentation Collection

The consolidation of scientific knowledge proceeds through the interpretation and then distillation of data presented in research reports, first in review articles and then in textbooks and undergraduate courses, until truths become accepted as such both amongst “experts” and in the public understanding. Where data are collected but remain unpublished, they cannot contribute to this distillation of knowledge. If these unpublished data differ substantially from published work, conclusions may not reflect adequately the underlying biological effects being described. The existence and any impact of such “publication bias” in the laboratory sciences have not been described. Using the CAMARADES (Collaborative Approach …

An Analysis Of Nonignorable Nonresponse In A Survey With A Rotating Panel Design, Caterina Giusti, Roderick J. Little

The University of Michigan Department of Biostatistics Working Paper Series

Missing values to income questions are common in survey data. When the probabilities of nonresponse are assumed to depend on the observed information and not on the underlining unobserved amounts, the missing income values are missing at random (MAR), and methods such as sequential multiple imputation can be applied. However, the MAR assumption is often considered questionable in this context, since missingness of income is thought to be related to the value of income itself, after conditioning on available covariates. In this article we describe a sensitivity analysis based on a pattern-mixture model for deviations from MAR, in the context …

Statistical Learning And Behrens-Fisher Distribution Methods For Heteroscedastic Data In Microarray Analysis, Nabin K. Manandhr-Shrestha

USF Tampa Graduate Theses and Dissertations

The aim of the present study is to identify the di®erentially expressed genes be- tween two di®erent conditions and apply it in predicting the class of new samples using the microarray data. Microarray data analysis poses many challenges to the statis- ticians because of its high dimensionality and small sample size, dubbed as "small n large p problem". Microarray data has been extensively studied by many statisticians and geneticists. Generally, it is said to follow a normal distribution with equal vari- ances in two conditions, but it is not true in general. Since the number of replications is very small, …

Panel Count Data Regression With Informative Observation Times, Petra Buzkova

UW Biostatistics Working Paper Series

When patients are monitored for potentially recurrent events such as infections or tumor metastases, it is common for clinicians to ask patients to come back sooner for follow-up based on the results of the most recent exam. This means that subjects’ observation times will be irregular and related to subject-specific factors. Previously proposed methods for handling such panel count data assume that the dependence between the events process and the observation time process is time-invariant. This article considers situations where the observation times are predicted by time-varying factors, such as the outcome observed at the last visit or cumulative exposure. …

Extensions Of Nearest Shrunken Centroid Method For Classification, Tomohiko Funai

Theses and Dissertations

Stylometry assumes that the essence of the individual style of an author can be captured using a number of quantitative criteria, such as the relative frequencies of noncontextual words (e.g., or, the, and, etc.). Several statistical methodologies have been developed for authorship analysis. Jockers et al. (2009) utilize Nearest Shrunken Centroid (NSC) classification, a promising classification methodology in DNA microarray analysis for authorship analysis of the Book of Mormon. Schaalje et al. (2010) develop an extended NSC classification to remedy the problem of a missing author. Dabney (2005) and Koppel et al. (2009) suggest other modifications of NSC. This paper …