Journal of Mathematical Sciences

, Volume 75, Issue 2, pp 1518–1523 | Cite as

Estimating the probability density function of a shift parameter

  • M. Ya. Penskaya
Point and Interval Estimation


The kernel estimators of a prior density function of a shift parameter are proposed. The upper and lower bounds for the mean square error of these estimates are evaluated.


Density Function Probability Density Lower Bound Probability Density Function Kernel Estimator 
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  1. 1.
    I. E. Simonova, “Application of the regularization method to distribution estimation,”Zh. Vychisl. Mat., Mat. Fiz.,22, No. 4, 801–813 (1982).MATHMathSciNetGoogle Scholar
  2. 2.
    T. O’Bryan and G. Walter, “Mean square estimation of the prior distribution,”Sankhya,41, Nos. A1–A2, 95–108 (1979).MathSciNetGoogle Scholar
  3. 3.
    V. B. Ilyushin, “Statistical estimate for the component of convolution of probability distribution,”Integral and Measure: collection of Scientific Works by Different Institutes [in Russian], Kuibyshev Univ. Press, Kuibyshev, 30–34 (1982).Google Scholar
  4. 4.
    L. V. Revishvili, “Estimating prior density by the regularization method of A.N.Tikhonov,”Soobshch. Akad. Nauk GSSR,86, No. 1, 41–44 (1977).MATHGoogle Scholar
  5. 5.
    W. R. Gaffey, “A consistent estimation of a component of convolution,”Ann. Math. Stat.,30, No. 1, 198–205 (1959).MATHMathSciNetGoogle Scholar
  6. 6.
    E. Parzen, “On estimation of a probability density function and mode,”Ann. Math. Stat.,33, No. 3, 1065–1076 (1962).MATHMathSciNetGoogle Scholar
  7. 7.
    E. A. Nadaraya,Nonparametric Estimation of Probability Densities and Regression Curves, Kluwer Academic Publ. Group, Dordrecht (1983).Google Scholar
  8. 8.
    M. V. Fedoriuk,Saddle-Point Method [in Russian], Nauka, Moscow (1977).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • M. Ya. Penskaya
    • 1
  1. 1.Perm

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