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1993-1995 | 22 | 1 | 103-115
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
22
Numer
1
Strony
103-115
Opis fizyczny
Daty
wydano
1993
otrzymano
1993-3-4
Twórcy
  • Department of Mathematics and Statistics, UMBC, Baltimore, Maryland 21228, U.S.A.
Bibliografia
  • [1] D. E. Barton, Unbiased estimation of a set of probabilities, Biometrika 48 (1961), 227-229.
  • [2] A. P. Basu, Estimates of reliability for some distributions useful in life testing, Technometrics 6 (1964), 215-219.
  • [3] N. Bingham, C. Goldie and J. Teugels, Regular Variation, Encyclopedia Math. Appl., Cambridge University Press, Cambridge, 1987.
  • [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.
  • [5] L. D. Brown, Fundamentals of Statistical Exponential Families with Applications in Statistical Decision Theory, Institute of Mathematical Statistics, Lecture Notes-Monograph Series, Volume 9, Hayward, CA, 1968.
  • [6] J. Folks, D. A. Pierce and C. Stewart, Estimating the fraction of acceptable product, Technometrics 7 (1965), 43-50.
  • [7] I. Gertsbakh and A. Winterbottom, Point and interval estimation of normal tail probabilities, Comm. Statist. Theory Methods 4 (1991), 1497-1514.
  • [8] W. C. Geunther, A note on the minimum variance unbiased estimate of the fraction of a normal distribution below a specification limit, Amer. Statist. 25 (1971), 18-20.
  • [9] L. B. Klebanov, Unbiased parametric distribution estimation, Mat. Zametki 25 (1979), 743-750 (in Russian).
  • [10] A. N. Kolmogorov, Unbiased estimates, Izv. Akad. Nauk SSSR Ser. Mat. 14 (1950), 303-326 (in Russian).
  • [11] E. L. Lehmann, Theory of Point Estimation, Wiley, New York, 1983.
  • [12] G. J. Lieberman and G. J. Resnikoff, Sampling plans for inspections by variables, J. Amer. Statist. Assoc. 50 (1955), 457-516.
  • [13] A. L. Rukhin, Estimating normal tail probabilities, Naval Res. Logist. Quart. 33 (1986), 91-99.
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv22i1p103bwm
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