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Simultaneous estimation of restricted means via the gauss divergence theorem

Abstract

This paper addresses the problem of estimating means of Hudson (1978) type exponential families, where the vector of means lies in a closed convex set with a piecewise smooth boundary. Instead of Stein (1981)-like integration-by-parts technique, the Gauss divergence theorem is used to provide an inequality for evaluation of the risk function with respect to a quadratic loss. The inequality shows that a James and Stein (1961) type estimator is superior to the least squares estimator subject to restriction on the closed convex set.

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Correspondence to Hisayuki Tsukuma.

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Tsukuma, H. Simultaneous estimation of restricted means via the gauss divergence theorem. Sankhya A 73, 110–124 (2011). https://doi.org/10.1007/s13171-011-0001-5

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  • DOI: https://doi.org/10.1007/s13171-011-0001-5

AMS (2000) subject classification

  • Primary 62H12, 62F30
  • Secondary 62J07

Keywords and phrases

  • Decision theory
  • divergence theorem
  • James-Stein’s estimator
  • quadratic loss
  • restricted parameter space
  • simultaneous estimation