Date of Graduation

12-2020

Document Type

Thesis

Degree Name

Master of Science in Statistics and Analytics (MS)

Degree Level

Graduate

Department

Statistics and Analytics

Advisor/Mentor

Qingyang Zhang

Committee Member

Mark E. Arnold

Second Committee Member

Giovanni Petris

Keywords

Biweight midcorrelation, Copula correlation, Distance correlation, Maximal information coefficient correlation, Mutual information, Spearman’s correlation

Abstract

Measuring and testing dependence between random variables is of great importance in many scientific fields. In the case of linearly correlated variables, Pearson’s correlation coefficient is a commonly used measure of the correlation strength. In the case of nonlinear correlation, several innovative measures have been proposed, such as distance-based correlation, rank-based correlations, and information theory-based correlation. This thesis focuses on the statistical comparison of several important correlations, including Spearman’s correlation, mutual information, maximal information coefficient, biweight midcorrelation, distance correlation, and copula correlation, under various simulation settings such as correlative patterns and the level of random noise. Furthermore, we apply those correlations with the overall best performance to a real genomic data set, to study the co-expression between genes in serous ovarian cancer.

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