題 目：Shrinkage Estimators for the Mean Matrix of a Multivariate
Complex Normal Distribution
主講人： Prof. Yoshihiko Konno(今野良彦) (Japan Women’s University, Japan)
時 間：101年12月5日(星期三)下午13:30-14:20
地 點：交大綜合一館427室
Abstract
Lillestøl (1977) investigated Stein-like shrinkage estimators for the mean
vector of a complex normal model. However, the shrinkage methods for this
model have received less attention so far, although it is important to
develop these methods beyond the maximum likelihood estimator of the unknown
signals in the multivariate complex normal distribution. The goal of this
talk is to show how certain decision theoretical results concerning the
problem of estimating a mean matrix of the real normal distribution can be
extended to the complex multivariate normal case. The problem of estimating a
mean matrix of a multivariate complex normal distribution with an unknown
covariance matrix is considered under an invariant loss function. By using
complex versions of the Stein identity and the Stein-Haidentity, a formula
is obtained for an unbiased estimate of the risk of an invariant
class of estimators, from which several minimax shrinkage estimators are
constructed.
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