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      A Derivation of the Wishart and Singular Wishart Distributions

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      STACK-THESIS-2016.pdf (477.0Kb)
      Date
      2016-08-23
      Author
      Stack, Karly L 1992-
      Type
      Thesis
      Degree Level
      Masters
      Metadata
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      Abstract
      Multivariate statistical analysis is the area of statistics that is concerned with observations made on many variables. Determining how variables are related is a main objective in multivariate analysis. The covariance matrix is an essential part of understanding the dependence between variables. The distribution of the sample covariance matrix for a sample from a multivariate normal distribution, known as the Wishart distribution, is fundamental to multivariate statistical analysis. An important assumption of the well-known Wishart distribution is that the number of variables is smaller than the number of observations. In high-dimensions when the number of variables exceeds the number of observations, the Wishart matrix is singular and has a singular Wishart distribution. The purpose of this research is to rederive the Wishart and singular Wishart distributions and understand the mathematics behind each derivation.
      Degree
      Master of Science (M.Sc.)
      Department
      Mathematics and Statistics
      Program
      Mathematics
      Supervisor
      Szmigielski, Jacek
      Committee
      Soteros, Chris; Sarty, Gordon; Samei, Ebrahim
      Copyright Date
      October 2016
      URI
      http://hdl.handle.net/10388/7402
      Subject
      Wishart
      singular Wishart
      anti-Wishart
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