Estimating normal density and normal distribution function: is Kolmogorov's estimator admissible?

Andrew Rukhin

Applicationes Mathematicae (1993)

  • Volume: 22, Issue: 1, page 103-115
  • ISSN: 1233-7234

Abstract

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The statistical estimation problem of the normal distribution function and of the density at a point is considered. The traditional unbiased estimators are shown to have Bayes nature and admissibility of related generalized Bayes procedures is proved. Also inadmissibility of the unbiased density estimator is demonstrated.

How to cite

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Rukhin, Andrew. "Estimating normal density and normal distribution function: is Kolmogorov's estimator admissible?." Applicationes Mathematicae 22.1 (1993): 103-115. <http://eudml.org/doc/219074>.

@article{Rukhin1993,
abstract = {The statistical estimation problem of the normal distribution function and of the density at a point is considered. The traditional unbiased estimators are shown to have Bayes nature and admissibility of related generalized Bayes procedures is proved. Also inadmissibility of the unbiased density estimator is demonstrated.},
author = {Rukhin, Andrew},
journal = {Applicationes Mathematicae},
keywords = {point estimation; normal density; Bayes estimator; quadratic loss; admissibility; normal distribution function; conjugate priors; scale equivariant procedures; normal distribution; unbiased estimators; generalized Bayes procedures; inadmissiblity of the unbiased density estimator},
language = {eng},
number = {1},
pages = {103-115},
title = {Estimating normal density and normal distribution function: is Kolmogorov's estimator admissible?},
url = {http://eudml.org/doc/219074},
volume = {22},
year = {1993},
}

TY - JOUR
AU - Rukhin, Andrew
TI - Estimating normal density and normal distribution function: is Kolmogorov's estimator admissible?
JO - Applicationes Mathematicae
PY - 1993
VL - 22
IS - 1
SP - 103
EP - 115
AB - The statistical estimation problem of the normal distribution function and of the density at a point is considered. The traditional unbiased estimators are shown to have Bayes nature and admissibility of related generalized Bayes procedures is proved. Also inadmissibility of the unbiased density estimator is demonstrated.
LA - eng
KW - point estimation; normal density; Bayes estimator; quadratic loss; admissibility; normal distribution function; conjugate priors; scale equivariant procedures; normal distribution; unbiased estimators; generalized Bayes procedures; inadmissiblity of the unbiased density estimator
UR - http://eudml.org/doc/219074
ER -

References

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  3. [3] N. Bingham, C. Goldie and J. Teugels, Regular Variation, Encyclopedia Math. Appl., Cambridge University Press, Cambridge, 1987. Zbl0617.26001
  4. [4] G. G. Brown and H. C. Rutemiller, The efficiencies of maximum likelihood and minimum variance unbiased estimators of fraction defective in the normal case, Technometrics 15 (1973), 849-855. Zbl0269.62030
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  9. [9] L. B. Klebanov, Unbiased parametric distribution estimation, Mat. Zametki 25 (1979), 743-750 (in Russian). 
  10. [10] A. N. Kolmogorov, Unbiased estimates, Izv. Akad. Nauk SSSR Ser. Mat. 14 (1950), 303-326 (in Russian). Zbl0039.15102
  11. [11] E. L. Lehmann, Theory of Point Estimation, Wiley, New York, 1983. Zbl0522.62020
  12. [12] G. J. Lieberman and G. J. Resnikoff, Sampling plans for inspections by variables, J. Amer. Statist. Assoc. 50 (1955), 457-516. Zbl0064.38602
  13. [13] A. L. Rukhin, Estimating normal tail probabilities, Naval Res. Logist. Quart. 33 (1986), 91-99. Zbl0601.62036
  14. [14] S. Zacks, The Theory of Statistical Inference, Wiley, New York, 1971. 
  15. [15] S. Zacks and R. C. Milton, Mean square errors of the best unbiased and maximum likehood estimators of tail probabilities in normal distributions, J. Amer. Statist. Assoc. 66 (1971), 590-593. Zbl0222.62010

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