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Some biased estimates of the mean of the normal distribution

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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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References

  1. Bateman Manuscript Project (1953).Higher Transcendental Functions,2, McGraw-Hill Book Co.

    Google Scholar 

  2. Cohen, A. (1965). Estimate of linear combinations of the parameters in the mean vector of a multivariate distribution,Ann. Math. Statist.,36, 78–87.

    MATH  MathSciNet  Google Scholar 

  3. Karlin, S. (1958). Admissibility for estimation with quadratic loss,Ann. Math. Statist.,29, 406–436.

    MATH  MathSciNet  Google Scholar 

  4. National Bureau of Standards, Applied Mathematics Series 55 (1964).Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables.

  5. Sacks, J. (1963). Generalized Bayes solutions in estimation problems,Ann. Math. Statist.,34, 751–768.

    MATH  MathSciNet  Google Scholar 

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Additional information

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

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