Keywords
Limiting spectral distribution, Marˇcenko-Pastur law, Heavy-Tailed distributions, method of moments.
Abstract
This major paper offers an extensive review of literature concerning the limiting distributions for the eigenvalue spectrum of sample correlation matrices from a p-dimensional population, where both the dimension p and the sample size n grow to infinity. The study systematically categorizes the reviewed literature based on underlying assumptions regarding the data characteristics. Specifically, it examines several distinct cases: the independent and identically distributed (i.i.d) case with finite fourth moments, the i.i.d case with infinite fourth moments, the i.i.d case with infinite second moments, and scenarios where rows and columns of the data are linearly dependent. Additionally, the major paper provides brief insights into the methodologies employed in the reviewed papers, offering a glimpse into the diverse analytical techniques utilized to investigate the limiting distributions of eigenvalues in correlation matrices.
Primary Advisor
Dr. Sévérien Nkurunziza
Program Reader
Dr. Mohamed Belalia
Degree Name
Master of Science
Department
Mathematics and Statistics
Document Type
Major Research Paper
Convocation Year
2024
Included in
Probability Commons, Statistical Methodology Commons, Statistical Models Commons, Statistical Theory Commons