Statistical Theory Commons^™

On M-Estimation: From Theory To Examples, Alexander Yuan

Master's Theses

M-estimation provides a unified framework for statistical procedures defined as optimizers of data-dependent criterion functions. This thesis gives an expository account of M-estimation in classical and high-dimensional settings. The classical part develops weak convergence, empirical process tools, and the argmax framework for studying consistency, rates of convergence, and weak limits. Examples including least squares, maximum likelihood, robust location estimation, change-point estimation, and empirical risk minimization illustrate regular and non-regular asymptotic behavior.

The high-dimensional part studies regularized M-estimators, where the focus shifts to finite-sample error bounds and model selection guarantees. Topics include decomposable regularizers, restricted strong convexity, non-convex penalties, and sparsistency. …

A Study Of The Parametric And Nonparametric Linear-Circular Correlation Coefficient, Robin Tu

Statistics

Circular statistics are specialized statistical methods that deal specifically with directional data. Data that is angular require specialized techniques due to the modulo 2π (in radians) or modulo 360^◦ (in degrees) nature of angles.

Correlation, typically in terms of Pearson’s correlation coefficient, is a measure of association between two linear random variables x and y. In this paper, the specific circular technique of the parametric and nonparametric linear-circular correlation coefficient will be explored where correlation is no longer between two linear variables x and y, but between a linear random variable x and circular random variable θ.

A simulation …

Adaptive Randomization Designs, Jenna Colavincenzo

Statistics

Adaptive design methodologies use prior information to develop a clinical trial design. The goal of an adaptive design is to maintain the integrity and validity of the study while giving the researcher flexibility in identifying the optimal treatment. An example of an adaptive design can be seen in a basic pharmaceutical trial. There are three phases of the overall trial to compare treatments and experimenters use the information from the previous phase to make changes to the subsequent phase before it begins.

Adaptive design methods have been in practice since the 1970s, but have become increasingly complex ever since. One …

Using The R Library Rpanel For Gui-Based Simulations In Introductory Statistics Courses, Ryan M. Allison

Statistics

As a student, I noticed that the statistical package R (http://www.r-project.org) would have several benefits of its usage in the classroom. One benefit to the package is its free and open-source nature. This would be a great benefit for instructors and students alike since it would be of no cost to use, unlike other statistical packages. Due to this, students could continue using the program after their statistical courses and into their professional careers. It would be good to expose students while they are in school to a tool that professionals use in industry. R also has powerful …