Statistical Applications of Jordan Algebras (Paperback, Softcover reprint of the original 1st ed. 1994)

This monograph brings together my work in mathematical statistics as I have viewed it through the lens of Jordan algebras. Three technical domains are to be seen: applications to random quadratic forms (sums of squares), the investigation of algebraic simplifications of maxi mum likelihood estimation of patterned covariance matrices, and a more wide open mathematical exploration of the algebraic arena from which I have drawn the results used in the statistical problems just mentioned. Chapters 1, 2, and 4 present the statistical outcomes I have developed using the algebraic results that appear, for the most part, in Chapter 3. As a less daunting, yet quite efficient, point of entry into this material, one avoiding most of the abstract algebraic issues, the reader may use the first half of Chapter 4. Here I present a streamlined, but still fully rigorous, definition of a Jordan algebra (as it is used in that chapter) and its essential properties. These facts are then immediately applied to simplifying the M: -step of the EM algorithm for multivariate normal covariance matrix estimation, in the presence of linear constraints, and data missing completely at random. The results presented essentially resolve a practical statistical quest begun by Rubin and Szatrowski 1982], and continued, sometimes implicitly, by many others. After this, one could then return to Chapters 1 and 2 to see how I have attempted to generalize the work of Cochran, Rao, Mitra, and others, on important and useful properties of sums of squares."

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Lecture Notes in Statistics, 91
Release date:	August 1994
First published:	August 1994
Authors:	James D Malley
Dimensions:	235 x 155 x 6mm (L x W x T)
Format:	Paperback
Pages:	102
Edition:	Softcover reprint of the original 1st ed. 1994
ISBN-13:	978-0-387-94341-1
Categories:	Books > Science & Mathematics > Mathematics > Probability & statistics Books > Science & Mathematics > Mathematics > Algebra > General Promotions
LSN:	0-387-94341-2
Barcode:	9780387943411

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