Statistics and Probability Commons^™

Functional Data Analysis Of Covid-19, Nichole L. Fluke

Mathematics & Statistics ETDs

This thesis deals with Functional Data Analysis (FDA) on COVID data. The Data involves counts for new COVID cases, hospitalized COVID patients, and new COVID deaths. The data used is for all the states and regions in the United States. The data starts in March 1^st, 2020 and goes through March 31^st, 2021. The FDA smooths the data and looks to see if there are similarities or differences between the states and regions in the data. The data also shows which states and regions stand out from the others and which ones are similar. Also shown …

Statistical Extensions Of Multi-Task Learning With Semiparametric Methods And Task Diagnostics, Nikolay Miller

Mathematics & Statistics ETDs

In this dissertation, I propose new approaches to multi-task learning, inspired by statistical model diagnostics and semiparametric and additive modeling. The newly designed additive multi-task model framework allows for flexible estimation of multi-task parametric and nonparametric effects by using an extension of the backfitting algorithm. Further, I propose new methods for statistical task diagnostics, which allow for the identification and remedy of outlier tasks, based on task-specific performance metrics and their empirical distributions. I perform a deep examination of the well-established multi-task kernel method and achieve theoretical and experimental contributions. Lastly, I propose a two-step modeling approach to multi-task modeling, …

Contributions To Statistical Testing, Prediction, And Modeling, John C. Pesko

Mathematics & Statistics ETDs

1. "Parametric Bootstrap (PB) and Objective Bayesian (OB) Testing with Applications to Heteroscedastic ANOVA": For one-way heteroscedastic ANOVA, we show a close relationship between the PB and OB approaches to significance testing, demonstrating the conditions for which the two approaches are equivalent. Using a simulation study, PB and OB performance is compared to a test based on the predictive distribution as well as the unweighted test of Akritas & Papadatos (2004). We extend this work to the RCBD with subsampling model, and prove a repeated sampling property and large sample property for general OB significance testing.

2. "Early Identification of …

Advanced Data Analysis - Lecture Notes, Erik B. Erhardt, Edward J. Bedrick, Ronald M. Schrader

Open Textbooks

Lecture notes for Advanced Data Analysis (ADA1 Stat 427/527 and ADA2 Stat 428/528), Department of Mathematics and Statistics, University of New Mexico, Fall 2016-Spring 2017. Additional material including RMarkdown templates for in-class and homework exercises, datasets, R code, and video lectures are available on the course websites: https://statacumen.com/teaching/ada1 and https://statacumen.com/teaching/ada2 .

Contents

I ADA1: Software

• 0 Introduction to R, Rstudio, and ggplot

II ADA1: Summaries and displays, and one-, two-, and many-way tests of means

• 1 Summarizing and Displaying Data
• 2 Estimation in One-Sample Problems
• 3 Two-Sample Inferences
• 4 Checking Assumptions
• 5 One-Way Analysis of Variance

III ADA1: Nonparametric, categorical, …

A General Procedure Of Estimating Population Mean Using Information On Auxiliary Attribute, Sachin Malik, Rajesh Singh, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper deals with the problem of estimating the finite population mean when some information on auxiliary attribute is available. It is shown that the proposed estimator is more efficient than the usual mean estimator and other existing estimators. The results have been illustrated numerically by taking empirical population considered in the literature.

A General Family Of Dual To Ratio-Cum-Product Estimator In Sample Surveys, Florentin Smarandache, Rajesh Singh, Mukesh Kumar, Pankaj Chauhan, Nirmala Sawan

Branch Mathematics and Statistics Faculty and Staff Publications

This paper presents a family of dual to ratio-cum-product estimators for the finite population mean. Under simple random sampling without replacement (SRSWOR) scheme, expressions of the bias and mean-squared error (MSE) up to the first order of approximation are derived. We show that the proposed family is more efficient than usual unbiased estimator, ratio estimator, product estimator, Singh estimator (1967), Srivenkataramana (1980) and Bandyopadhyaya estimator (1980) and Singh et al. (2005) estimator. An empirical study is carried out to illustrate the performance of the constructed estimator over others.