統計数学セミナー
Seminar on Probability and Statistics |
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Seminar on Probability and Statistics Wednesday December 5 2007 Tokyo 122 4:20-5:30 pm
A Decision-Theoretic Approach to Estimation from Wishart matrices on Symmetric Cones
今野 良彦 / KONNO, Yoshihiko 日本女子大学理学部 / Faculty of Science, Japan Women's University 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 algebras.
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