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

Applicationes Mathematicae (1993)

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

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topRukhin, 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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- [10] A. N. Kolmogorov, Unbiased estimates, Izv. Akad. Nauk SSSR Ser. Mat. 14 (1950), 303-326 (in Russian). Zbl0039.15102
- [11] E. L. Lehmann, Theory of Point Estimation, Wiley, New York, 1983. Zbl0522.62020
- [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] A. L. Rukhin, Estimating normal tail probabilities, Naval Res. Logist. Quart. 33 (1986), 91-99. Zbl0601.62036
- [14] S. Zacks, The Theory of Statistical Inference, Wiley, New York, 1971.
- [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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