Statistical applications of Jordan algebras
By: James D. Malley.
Series: Lecture notes in statistics ;; 91; Lecture notes in statistics (Springer-Verlag) ;; v. 91.
Publisher: Springer-Verlag; Springer
Published: 1994
Place of publication: New York
Language: eng
Number of pages: 102
Subjects: Jordan algebras.; Mathematical statistics.
Description: This volume brings together the author's work in mathematical statistics as viewed through the lens of Jordan algebras. In particular 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. This intertwining of ideas presented by the author will make this an interesting account suitable for researchers addressing these problems in statistics.
Notes: Includes bibliographical references and index.