| 书目名称 | Statistical Applications of Jordan Algebras | | 编辑 | James D. Malley | | 视频video | | | 丛书名称 | Lecture Notes in Statistics | | 图书封面 |  | | 描述 | 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 presen | | 出版日期 | Book 1994 | | 关键词 | Algebra; Covariance matrix; Likelihood; SAS; Variance; expectation–maximization algorithm; mathematical st | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4612-2678-9 | | isbn_softcover | 978-0-387-94341-1 | | isbn_ebook | 978-1-4612-2678-9Series ISSN 0930-0325 Series E-ISSN 2197-7186 | | issn_series | 0930-0325 | | copyright | Springer-Verlag New York, Inc. 1994 |
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发表于 2025-3-21 19:59:43
