Stein's idea and minimax admissible estimation of a multivariate normal mean

  • Authors:

  • Yuzo Maruyama

  • Affiliations:

  • Faculty of Economics, Center for Spatial Information Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku Tokyo 113-0033, Japan

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2004

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Abstract

We consider estimation of a multivariate normal mean vector under sum of squared error loss. We propose a new class of minimax admissible estimator which are generalized Bayes with respect to a prior distribution which is a mixture of a point prior at the origin and a continuous hierarchical type prior. We also study conditions under which these generalized Bayes minimax estimators improve on the James-Stein estimator and on the positive-part James-Stein estimator.