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  • © 1994

Statistical Applications of Jordan Algebras

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Part of the book series: Lecture Notes in Statistics (LNS, volume 91)

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  • ISBN: 978-1-4612-2678-9
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Table of contents (4 chapters)

  1. Front Matter

    Pages i-vi
  2. Introduction

    • James D. Malley
    Pages 1-4
  3. Further Technical Results on Jordan Algebras

    • James D. Malley
    Pages 42-62
  4. Back Matter

    Pages 96-105

About this book

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.

Keywords

  • Algebra
  • Covariance matrix
  • Likelihood
  • SAS
  • Variance
  • expectation–maximization algorithm
  • mathematical statistics

Authors and Affiliations

  • Division of Computer Research and Technology, National Institutes of Health, Bethesda, USA

    James D. Malley

Bibliographic Information

  • Book Title: Statistical Applications of Jordan Algebras

  • Authors: James D. Malley

  • Series Title: Lecture Notes in Statistics

  • DOI: https://doi.org/10.1007/978-1-4612-2678-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1994

  • Softcover ISBN: 978-0-387-94341-1

  • eBook ISBN: 978-1-4612-2678-9

  • Series ISSN: 0930-0325

  • Series E-ISSN: 2197-7186

  • Edition Number: 1

  • Number of Pages: VII, 102

  • Topics: Algebra, Probability Theory

Buying options

eBook USD 89.00
Price excludes VAT (USA)
  • ISBN: 978-1-4612-2678-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 119.99
Price excludes VAT (USA)