Discussiones Mathematicae Probability and Statistics 20(1) (2000) 51-62

NUMERICAL METHODS FOR LINEAR MINIMAX ESTIMATION

Norbert Gaffke and Berthold Heiligers

Fakultät für Mathematik, Institut für Mathematische Stochastik
Universität Magdeburg, D-39106 Magdeburg, Germany

Abstract

We discuss two numerical approaches to linear minimax estimation in linear models under ellipsoidal parameter restrictions. The first attacks the problem directly, by minimizing the maximum risk among the estimators. The second method is based on the duality between minimax and Bayes estimation, and aims at finding a least favorable prior distribution.

Keywords and phrases: Bayes estimation, duality, linear model, L-optimality, mean squared error, minimax estimation, non-smooth optimization, parameter restrictions, p-mean, quasi Newton method.

1991 Mathematics Subject Classification: 62F10, 62J05.

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Received 25 November 1998