Statistical Applications of Jordan Algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1994
|
| Schriftenreihe: | Lecture Notes in Statistics
91 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (VII, 102p) |
| ISBN: | 9781461226789 9780387943411 |
| ISSN: | 0930-0325 |
| DOI: | 10.1007/978-1-4612-2678-9 |
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Datensatz im Suchindex
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-2678-9 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461226789 9780387943411 |
| issn | 0930-0325 |
| language | English |
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| spelling | Malley, James D. Verfasser aut Statistical Applications of Jordan Algebras by James D. Malley New York, NY Springer New York 1994 1 Online-Ressource (VII, 102p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Statistics 91 0930-0325 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 Mathematics Algebra Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Jordan-Algebra (DE-588)4162770-2 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Jordan-Algebra (DE-588)4162770-2 s Statistik (DE-588)4056995-0 s 1\p DE-604 https://doi.org/10.1007/978-1-4612-2678-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Malley, James D. Statistical Applications of Jordan Algebras Mathematics Algebra Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Jordan-Algebra (DE-588)4162770-2 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4162770-2 (DE-588)4056995-0 |
| title | Statistical Applications of Jordan Algebras |
| title_auth | Statistical Applications of Jordan Algebras |
| title_exact_search | Statistical Applications of Jordan Algebras |
| title_full | Statistical Applications of Jordan Algebras by James D. Malley |
| title_fullStr | Statistical Applications of Jordan Algebras by James D. Malley |
| title_full_unstemmed | Statistical Applications of Jordan Algebras by James D. Malley |
| title_short | Statistical Applications of Jordan Algebras |
| title_sort | statistical applications of jordan algebras |
| topic | Mathematics Algebra Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Jordan-Algebra (DE-588)4162770-2 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Mathematics Algebra Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Jordan-Algebra Statistik |
| url | https://doi.org/10.1007/978-1-4612-2678-9 |
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