Mathematics Commons^™

An Interval-Valued Random Forests, Paul Gaona Partida

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

There is a growing demand for the development of new statistical models and the refinement of established methods to accommodate different data structures. This need arises from the recognition that traditional statistics often assume the value of each observation to be precise, which may not hold true in many real-world scenarios. Factors such as the collection process and technological advancements can introduce imprecision and uncertainty into the data.

For example, consider data collected over a long period of time, where newer measurement tools may offer greater accuracy and provide more information than previous methods. In such cases, it becomes crucial …

Estimating The Extreme Low-Temperature Event Using Nonparametric Methods, Anisha D'Silva

Master's Theses (2009 -)

This thesis presents a new method of estimating the one-in-N low temperature threshold using a non-parametric statistical method called kernel density estimation applied to daily average wind-adjusted temperatures. We apply our One-in-N Algorithm to local gas distribution companies (LDCs), as they have to forecast the daily natural gas needs of their consumers. In winter, demand for natural gas is high. Extreme low temperature events are not directly related to an LDCs gas demand forecasting, but knowledge of extreme low temperatures is important to ensure that an LDC has enough capacity to meet customer demands when extreme low temperatures are experienced. …

Methods Of Nonparametric Multivariate Ranking And Selection, Jeremy Entner

Mathematics - Dissertations

In a Ranking and Selection problem, a collection of k populations is given which follow some (partially) unknown probability distributions. The problem is to select the "best" of the k populations where "best" is well defined in terms of some unknown population parameter. In many univariate parametric and nonparamentric settings, solutions to these ranking and selection problems exist. In the multivariate case, only parametric solutions have been developed. We have developed several methods for solving nonparametric multivariate ranking and selection problems. The problems considered allow an experimenter to select the "best" populations based on nonparametric notions of dispersion, location, and …

Using Correlation Coefficients To Estimate Slopes In Multiple Linear Regression, Rudy Gideon

Mathematical Sciences Faculty Publications

This short note takes correlation coefficients as the starting point to obtain inferential results in linear regression. Under certain conditions, the population correlation coefficient and the sampling correlation coefficient can be related via a Taylor series expansion to allow inference on the coefficients in simple and multiple regression. This general method includes nonparametric correlation coefficients and so gives a universal way to develop regression methods. This work is part of a correlation estimation system that uses correlation coefficients to perform estimation in many settings, for example, time series, nonlinear and generalized linear models, and individual distributions.

Extending The Skill Test For Disease Diagnosis, Shu-Chuan Lin, Paul H. Kvam, Jye-Chyi Lu

Department of Math & Statistics Faculty Publications

For diagnostic tests, we present an extension to the skill plot introduced by Briggs and Zaretski (Biometrics 2008; 64:250–261). The method is motivated by diagnostic measures for osteopetrosis in a study summarized by Hans et al. (The Lancet 1996; 348:511–514). Diagnostic test accuracy is typically defined using the area (or partial area) under the receiver operator characteristic (ROC) curve. If partial area is used, the resulting statistic can be highly subjective because the focus region of the ROC curve corresponds to a set of low false‐positive rates that are chosen by the experimenter. This paper introduces a more …

Length Bias In The Measurements Of Carbon Nanotubes, Paul H. Kvam

Department of Math & Statistics Faculty Publications

To measure carbon nanotube lengths, atomic force microscopy and special software are used to identify and measure nanotubes on a square grid. Current practice does not include nanotubes that cross the grid, and, as a result, the sample is length-biased. The selection bias model can be demonstrated through Buffon’s needle problem, extended to general curves that more realistically represent the shape of nanotubes observed on a grid. In this article, the nonparametric maximum likelihood estimator is constructed for the length distribution of the nanotubes, and the consequences of the length bias are examined. Probability plots reveal that the corrected length …

A Conversation With R. Clifford Blair On The Occasion Of His Retirement, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

An interview was conducted on 23 November 2003 with R. Clifford Blair on the occasion on his retirement from the University of South Florida. This article is based on that interview. Biographical sketches and images of members of his academic genealogy are provided.

A Comparison Of Two Linear Nonparametric Regression Techniques, Sylvain Sardy

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This thesis presented a useful tool in regression. Nonparametric linear regression techniques were described in the general context of regression. A comparison of two of these techniques, kernel regression and iterative regression, showed various aspects of nonparametric linear regressors.

A Monte Carlo Evaluation Of A Nonparametric Technique For Estimating The Hazard Function, Sheng Jia Lin

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This research is primarily concerned with the estimation of the Hazard functions, the Hazard function is the failure rate at time t, and is defined as -R '(t)/R(t), so it plays an important role in Reliability.

In order to compare and evaluate the estimation methods, it is convenient to select one distribution in this research. Since the Weibull distribution is a useful distribution in Reliability, the Weibull distribution is used in this paper.