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Estimating one of two normal means when their difference is bounded

✍ Scribed by Constance van Eeden; James V. Zidek

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
104 KB
Volume
51
Category
Article
ISSN
0167-7152

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✦ Synopsis

In this paper, we address the problem of estimating Γ‚1 when Yj ∼ ind N(Γ‚j; 2 j ); j = 1; 2, are observed, the j are known and |Γ‚1 -Γ‚2|6c for a known constant c. Assuming the loss is squared error, we derive a generalized Bayes estimator which is admissible. It uses Y2 to achieve a uniformly smaller risk than that of the classical UMVU estimator, Y1. The proofs use a combination of Stein and Kubokawa methods.

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