Term of Award
Spring 2021
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Department of Mathematical Sciences
Committee Chair
Stephen Carden
Committee Member 1
Arpita Chatterjee
Committee Member 2
Divine Wanduku
Abstract
This thesis project will analyze the bias in mixture models when contaminated data is present. Specifically, we will analyze the relationship between the bias and the mixing proportion, p, for the rank correlation methods Spearman’s Rho and Kendall’s Tau. We will first look at the history of the two non-parametric rank correlation methods and the sample and population definitions will be introduced. Copulas will be introduced to show a few ways we can define these correlation methods. After that, mixture models will be defined and the main theorem will be stated and proved. As an example, we will apply this theorem to the Marshall-Olkin distribution. This will allow us to show the bias graphically for each of the different correlation methods.
OCLC Number
1249448126
Catalog Permalink
https://galileo-georgiasouthern.primo.exlibrisgroup.com/permalink/01GALI_GASOUTH/1r4bu70/alma9916441248902950
Recommended Citation
Land, Russell, "Bias of Rank Correlation Under A Mixture Model" (2021). Electronic Theses and Dissertations. 2212.
https://digitalcommons.georgiasouthern.edu/etd/2212
Research Data and Supplementary Material
Yes
