| Statistical Applications of Jordan Algebras Softcover Repri Edition Contributor(s): Malley, James D. (Author) |
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ISBN: 0387943412 ISBN-13: 9780387943411 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback Published: August 1994 |
| Additional Information |
| BISAC Categories: - Mathematics | Group Theory - Mathematics | Probability & Statistics - General - Mathematics | Algebra - General |
| Dewey: 512.24 |
| LCCN: 94028225 |
| Series: Lecture Notes in Statistics |
| Physical Information: 0.24" H x 6.14" W x 9.21" (0.38 lbs) 102 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |