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Book by Malley James D
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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.
Reseña del editor
This volume brings together the author's work in mathematical statistics as viewed through the lens of Jordan algebras. In particular the three main areas covered in this work are: applications to random quadratic forms (sums of squares); the investigation of algebraic simplifications of maximum likelihood estimation of patterned covariance matrices; and a more wide-ranging mathematical exploration of some of the algebraic problems discussed. The author gives a full and rigorous definition of Jordan algebras and their essential properties and shows how they provide a natural and powerful algebraic tool for statisticians. In particular, the application of these methods to the M-step of the EM algorithm both simplifies this analysis and resolves some practical and important problems. This intertwining of ideas presented by the author will make this an interesting account suitable for researchers addressing these problems in statistics.
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- EditorialSpringer US
- Año de publicación1994
- ISBN 10 0387943412
- ISBN 13 9780387943411
- EncuadernaciónTapa blanda
- IdiomaInglés
- Número de páginas118
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Statistical applications of Jordan algebras Lecture notes in statistics ; Vol. 91
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New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest : Springer, 1994
ISBN 10: 0387943412
ISBN 13: 9780387943411
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Statistical Applications of Jordan Algebras (Lecture Notes in Statistics, 91)
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Statistical Applications of Jordan Algebras
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Springer New York Aug 1994, 1994
ISBN 10: 0387943412
ISBN 13: 9780387943411
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Taschenbuch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 116 pp. Englisch. Nº de ref. del artículo: 9780387943411
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Statistical Applications of Jordan Algebras (Lecture Notes in Statistics, 91)
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Statistical Applications of Jordan Algebras
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Springer New York, 1994
ISBN 10: 0387943412
ISBN 13: 9780387943411
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Kartoniert / Broschiert. Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 simpl. Nº de ref. del artículo: 5911969
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Statistical Applications of Jordan Algebras
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Springer New York, Springer US, 1994
ISBN 10: 0387943412
ISBN 13: 9780387943411
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Taschenbuch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Nº de ref. del artículo: 9780387943411
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Statistical Applications of Jordan Algebras
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Springer-Verlag New York Inc., 1994
ISBN 10: 0387943412
ISBN 13: 9780387943411
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Statistical Applications of Jordan Algebras
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Statistical Applications of Jordan Algebras
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Statistical Applications of Jordan Algebras
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