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Item Details
Title:
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STATISTICAL APPLICATIONS OF JORDAN ALGEBRAS
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By: |
James D. Malley |
Format: |
Paperback |
List price:
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£89.99 |
We currently do not stock this item, please contact the publisher directly for
further information.
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ISBN 10: |
0387943412 |
ISBN 13: |
9780387943411 |
Publisher: |
SPRINGER-VERLAG NEW YORK INC. |
Pub. date: |
25 August, 1994 |
Edition: |
Softcover reprint of the original 1st ed. 1994 |
Series: |
Lecture Notes in Statistics 91 |
Pages: |
109 |
Synopsis: |
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. |
Illustrations: |
biography |
Publication: |
US |
Imprint: |
Springer-Verlag New York Inc. |
Returns: |
Returnable |
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