Summary
LetX be normally distributed with mean θ and variance σ2. We consider the problem of estimating θ with squared error as the loss function. A priori the true value of θ is known to be close to θ0, say. Several estimates are considered which might be preferred toX, the unbiased estimate of θ, as their risks are smaller in the neighborhood of θ0. The admissibility of these estimates is discussed in this paper.
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This research was supported in part by ONR Grants NR-042-271 and NR-042-283 at Clemson University and Rice University respectively.
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Alam, K., Thompson, J.R. Some biased estimates of the mean of the normal distribution. Ann Inst Stat Math 25, 57–64 (1973). https://doi.org/10.1007/BF02479359
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DOI: https://doi.org/10.1007/BF02479359