Physical Sciences and Mathematics Commons^™

Nonparametric Methods For Analysis And Sizing Of Cluster Randomization Trials With Baseline Measurements, Chengchun Yu

Electronic Thesis and Dissertation Repository

Cluster randomization trials are popular in situations where the intervention needs to be implemented at the cluster level, or logistical, financial and/or ethical reason dictates the choice for randomization at the cluster level, or minimization of contamination is needed. It is very common for cluster trials to take measurements before randomization and again at follow-up, resulting in a clustered pretest-posttest design. For continuous outcomes, the cluster-adjusted analysis of covariance approach can be used to adjust for accidental bias and improve efficiency. However, a direct application of this method is nonsensical if the measures are incompatible with an interval scale, yet …

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 …

Nonparametric Estimation Of Elliptical Copulas, Panfeng Liang

Open Access Theses & Dissertations

Elliptical copulas provide flexibility in modeling the dependence structure of a random vector. They are often parameterized with a correlation matrix and a scalar function, called generator. The estimation of the generator can be challenging, because it is a functional parameter. In this dissertation, we provide a rigorous approach to estimating the generator in a Bayesian framework, which is simpler, more robust, and outperforms existing estimation methods in the literature. Based on the proposed framework in this dissertation, other researchers may modify the model for other types of generators in their own research.