Name: statistical applications of jordan algebras (en Inglés)
Price: 68.02 USD
Availability: InStock
Author: Malley, James D.
ISBN: 9780387943411

portada statistical applications of jordan algebras (en Inglés)

statistical applications of jordan algebras (en Inglés)

Formato

Libro Físico

Autor

James D. Malley

Editorial

Springer

Año

1994

Idioma

Inglés

N° páginas

102

Encuadernación

Tapa Blanda

Dimensiones

23.4 x 15.6 x 0.6 cm

Peso

0.17 kg.

ISBN

0387943412

ISBN13

9780387943411

Categorías

Álgebra
Grupos y teoría de grupos
Probabilidad y estadística

statistical applications of jordan algebras (en Inglés)

James D. Malley (Autor) · Springer · Tapa Blanda

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Reseña del libro "statistical applications of jordan algebras (en Inglés)"

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.