Ranking functions of data
department or school: Science, Irving K. Barber Faculty of (Okanagan)
department or school: Computer Science, Mathematics, Physics and Statistics, Department of (Okanagan)
data provider: DSpace
degree campus: UBCO
creator: Zhang, Cassie Yue
issued: 2023-11-16T20:56:39Z
issued: 2024
related degree: Master of Science - MSc
degree grantor: University of British Columbia
description: This thesis addresses a significant problem in numerous scientific fields - the challenge of determining whether two sets of data are statistically identical, a procedure known as a two-sample homogeneity test. Various methods, including well-known parametric tests like t-tests and analysis of variance (ANOVA), have been employed for two-sample homogeneity tests. However, these tests have certain limitations. They rely heavily on specific assumptions about the data's distribution. If these assumptions are violated, the results can be misleading. To overcome these limitations, non-parametric methods that do not require strict assumptions about the data's nature have been explored. However, these too have their shortcomings. For instance, techniques like the Wilcoxon rank-sum test can only be applied effectively in univariate cases, as multivariate data lacks a natural ranking. This complicates the analysis and limits the utility of such methods for multivariate data. In response to identified challenges, this work introduces an innovative approach to rank multivariate data through the concept of data depth. It encompasses a thorough comparison of eleven widely-used depth functions and the development of two novel two-sample homogeneity tests, significantly enhancing the accuracy of homogeneity assessments in multivariate datasets. Further, inspired by the quality index [25] used in quality assurance contexts to measure a population's overall 'outlyingness' relative to another, the proposed test statistics are designed to yield a 𝒳²(1) asymptotic null distribution. Simulation studies underscore the robust performance of these tests, and the discussion also extends into their potential application in multivariate multisample contexts, demonstrating the versatility and broad applicability of depth-based methodologies in statistical analysis. The increasing number of samples correspondingly increases the number of pairwise quality indexes, an aspect considered and explor…
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/86622
note: Ranking Functions of DatabyCassie Yue ZhangB.Sc., Thompson Rivers University, 2022M.Sc., The University of British Columbia, 2023A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE COLLEGE OF GRADUATE STUDIES(Mathematics)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)November 2023© Cassie Yue Zhang 2023The following individuals certify that they have read, and recommendto the College of Graduate Studies for acceptance, a thesis/dissertation en-titled:Ranking Functions of Datasubmitted by Cassie Yue Zhang in partial fulfilment of the requirementsof the degree of Master of ScienceDr. Xiaoping Shi, Department of Computer Science, Mathematics, Physics and StatisticsSupervisorDr. John Braun, Department of Computer Science, Mathematics, Physics and StatisticsSupervisory Committee MemberDr. Lengyi Han, Department of Computer Science, Mathematics, Physics and StatisticsSupervisory Committee MemberDr. Julian Cheng, School of EngineeringUniversity ExamineriiAbstractThis thesis addresses a significant problem in numerous scientific fields - thechallenge of determining whether two sets of data are statistically identical,a procedure known as a two-sample homogeneity test.Various methods, including well-known parametric tests like t-tests andanalysis of variance (ANOVA), have been employed for two-sample homo-geneity tests. However, these tests have certain limitations. They rely heav-ily on specific assumptions about the data’s distribution. If these assump-tions are violated, the results can be misleading.To overcome these limitations, non-parametric methods that do not re-quire strict assumptions about the data’s nature have been explored. How-ever, these too have their shortcomings. For instance, techniques like theWilcoxon rank-sum test can only be applied effectively in univariate cases,as multivariate data lacks a natural ranking. This complicates the analysisand limits the utility of such methods for multivariate data.In resp…
has type: Thesis/Dissertation
date issued: 2024-02
is shown at: 10.14288/1.0437696
language: eng
degree discipline: Mathematics
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Graduate
contributor: Xiaoping, Shi
type: Text
identifier URI: http://hdl.handle.net/2429/86622