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統計数学セミナー
過去の記録 ～04/19｜次回の予定｜今後の予定 04/20～
| 担当者 | 吉田朋広、荻原哲平、小池祐太 |
|---|---|
| セミナーURL | http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/ |
| 目的 | 確率統計学およびその関連領域に関する研究発表, 研究紹介を行う. |
2007年12月05日(水)
16:20-17:30 数理科学研究科棟(駒場) 122号室
今野 良彦 氏 (日本女子大学理学部)
A Decision-Theoretic Approach to Estimation from Wishart matrices on Symmetric Cones
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/11.html
今野 良彦 氏 (日本女子大学理学部)
A Decision-Theoretic Approach to Estimation from Wishart matrices on Symmetric Cones
[ 講演概要 ]
James and Stein(1961) have considered the problem of estimating the mean matrix of Wishart distributions under so-called Stein's loss function and obtained a minimax estimator with a constant risk. Later Stein(1977) has given an unbiased risk estimate for a class of orthogonally invariant estimators, from which he obtained orthogonally invariant minimax estimators which are uniformly better than the best triangular-invariant estimator in James and Stein(1961). The works mentioned above lead to the following natural question: Is it possible for any estimators to improve upon the maximum likelihood estimator for the mean matrix of the complex or quaternion Wishart distributions? This talk shows that we can obtain improved estimators for the mean matrix under these models in a unified manner. The method involves an abstract theory of finite-dimensional Euclidean simple Jordan algebra
[ 参考URL ]James and Stein(1961) have considered the problem of estimating the mean matrix of Wishart distributions under so-called Stein's loss function and obtained a minimax estimator with a constant risk. Later Stein(1977) has given an unbiased risk estimate for a class of orthogonally invariant estimators, from which he obtained orthogonally invariant minimax estimators which are uniformly better than the best triangular-invariant estimator in James and Stein(1961). The works mentioned above lead to the following natural question: Is it possible for any estimators to improve upon the maximum likelihood estimator for the mean matrix of the complex or quaternion Wishart distributions? This talk shows that we can obtain improved estimators for the mean matrix under these models in a unified manner. The method involves an abstract theory of finite-dimensional Euclidean simple Jordan algebra
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/11.html
