Minimax estimation of a multivariate normal mean under polynomial loss

James O. Berger

Journal of Multivariate Analysis, 1978, vol. 8, issue 2, 173-180

Abstract: Let X be an observation from a p-variate (p >= 3) normal random vector with unknown mean vector [theta] and known covariance matrix . The problem of improving upon the usual estimator of [theta], [delta]0(X) = X, is considered. An approach is developed which can lead to improved estimators, [delta], for loss functions which are polynomials in the coordinates of ([delta] - [theta]). As an example of this approach, the loss L([delta], [theta]) = [delta] - [theta]4 is considered, and estimators are developed which are significantly better than [delta]0. When is the identity matrix, these estimators are of the form [delta](X) = (1 - (b/(d + X2)))X.

Keywords: Multivariate; normal; distribution; polynomial; loss; risk; function; minimax; estimator (search for similar items in EconPapers)
Date: 1978
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Citations: View citations in EconPapers (1)

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