Journal of Mathematical Sciences

, Volume 88, Issue 6, pp 840–847 | Cite as

Kernel and pseudokernel estimators for the a priori density of a multivariate parameter

  • M. Ya. Penskaya
Point and Interval Estimation


Multivariate Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. Robbins, “An empirical Bayes approach to statistics,” in:Proceedings of the 3rd Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, Berkeley-Los Angeles (1959), pp. 157–163.Google Scholar
  2. 2.
    Ya. P. Lumel'skii, “Unbiased estimators for an a priori distribution and their applications,”Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 1, 80–89 (1973).MATHMathSciNetGoogle Scholar
  3. 3.
    W. R. Gaffey, “A consistent estimation of a component of a convolution,”Ann. Math. Statist,30, No. 1, 198–205 (1969).MathSciNetGoogle Scholar
  4. 4.
    G. G. Walter, “Orthogonal series estimators of a priori distribution,”Sankhya,A43, No. 2, 228–245 (1981).MATHGoogle Scholar
  5. 5.
    M. Ya. Penskaya, “Projective estimates for an a priori density and for the functionals depending on this density,” in:Probability Theory and Mathematical Statistics, Vol. 31 [in Russian], Kiev (1984), pp. 99–110.Google Scholar
  6. 6.
    M. Ya. Penskaya, “Estimation of an a priori density,”J. Sov. Math.,35, No. 2, 2381–2386 (1986).MATHGoogle Scholar
  7. 7.
    Zhang Cun-Hui, “Fourier methods for estimating mixing densities and distributions,”Ann. Statist.,18, No. 2, 806–831 (1990).MathSciNetGoogle Scholar
  8. 8.
    L. Stefanski and R. J. Carroll, “Deconvolving kernel density estimators,”Statistics,21, No. 2, 169–184 (1990).MathSciNetGoogle Scholar
  9. 9.
    M. Ya. Penskaya, “Estimating the probability density function of a shift parameter,”J. Math. Sci.,75, No. 2, 1518–1523 (1995).MathSciNetGoogle Scholar
  10. 10.
    J. R. Blum and V. Susarla, “Estimation of a mixing distribution function,”Ann. Probab.,5, No. 2, 200–209 (1977).MathSciNetGoogle Scholar
  11. 11.
    I. E. Simonova, “An application of the regularization method to distribution estimation,”J. Comput. Math. Math. Phys.,22, No. 4, 801–813 (1982).MATHMathSciNetGoogle Scholar
  12. 12.
    M. Ya. Penskaya, “An application of regulating operators in the statistical estimation theory,” in:Statistical Methods of Estimation and Testing Hypotheses [in Russian], Perm (1986), pp. 158–166.Google Scholar
  13. 13.
    T. O'Bryan and G. Walter, “Mean square estimation of a priori distribution,”Sankhya,A41, No. 1–2, 95–108 (1979).MathSciNetGoogle Scholar
  14. 14.
    R. J. Carroll and P. Hall, “Optimal rates of convergence for deconvolving a density,”J. Amer. Statist. Assoc.,83, No. 404, 1184–1186 (1988).MathSciNetGoogle Scholar
  15. 15.
    T. Cacoullos, “Estimation of a multivariate density,”Ann. Inst. Statist. Math.,18, 179–190 (1966).MATHMathSciNetGoogle Scholar
  16. 16.
    E. A. Nadaraya,Nonparametric Density and Regression Estimation [in Russian], Tbilisi Univ. Press, Tbilisi (1983).Google Scholar
  17. 17.
    I. S. Gradshtein and I. M. Ryzhik,Tables of Integrals Series and Products, Academic Press, New York (1980).Google Scholar
  18. 18.
    N. S. Bakhvalov,Numerical Methods [in Russian], Nauka, Moscow (1973).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • M. Ya. Penskaya
    • 1
  1. 1.PermRussia

Personalised recommendations