Synopsis
This volume brings together the author's work in mathematical statistics as viewed through the lens of Jordan algebras. The three main areas covered in this work are: applications to random quadratic forms (sums of squares); the investigation of algebraic simplifications of maximum likelihood estimation of patterned covariance matrices; and a more wide-ranging mathematical exploration of some of the algebraic problems discussed. The author gives a full and rigorous definition of Jordan algebras and their essential properties and shows how they provide a natural and powerful algebraic tool for statisticians. In particular, the application of these methods to the M-step of the EM algorithm both simplifies this analysis and resolves some practical and important problems.
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