Seminar on Probability and Statistics

Seminar information archive ~05/21Next seminarFuture seminars 05/22~

Organizer(s) Nakahiro Yoshida, Teppei Ogihara, Yuta Koike

2007/12/05

16:20-17:30   Room #122 (Graduate School of Math. Sci. Bldg.)
今野 良彦 (日本女子大学理学部)
A Decision-Theoretic Approach to Estimation from Wishart matrices on Symmetric Cones
[ Abstract ]
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
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/11.html