This is a preview of subscription content, log in via an institution to check access.
References
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.
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).
W. R. Gaffey, “A consistent estimation of a component of a convolution,”Ann. Math. Statist,30, No. 1, 198–205 (1969).
G. G. Walter, “Orthogonal series estimators of a priori distribution,”Sankhya,A43, No. 2, 228–245 (1981).
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.
M. Ya. Penskaya, “Estimation of an a priori density,”J. Sov. Math.,35, No. 2, 2381–2386 (1986).
Zhang Cun-Hui, “Fourier methods for estimating mixing densities and distributions,”Ann. Statist.,18, No. 2, 806–831 (1990).
L. Stefanski and R. J. Carroll, “Deconvolving kernel density estimators,”Statistics,21, No. 2, 169–184 (1990).
M. Ya. Penskaya, “Estimating the probability density function of a shift parameter,”J. Math. Sci.,75, No. 2, 1518–1523 (1995).
J. R. Blum and V. Susarla, “Estimation of a mixing distribution function,”Ann. Probab.,5, No. 2, 200–209 (1977).
I. E. Simonova, “An application of the regularization method to distribution estimation,”J. Comput. Math. Math. Phys.,22, No. 4, 801–813 (1982).
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.
T. O'Bryan and G. Walter, “Mean square estimation of a priori distribution,”Sankhya,A41, No. 1–2, 95–108 (1979).
R. J. Carroll and P. Hall, “Optimal rates of convergence for deconvolving a density,”J. Amer. Statist. Assoc.,83, No. 404, 1184–1186 (1988).
T. Cacoullos, “Estimation of a multivariate density,”Ann. Inst. Statist. Math.,18, 179–190 (1966).
E. A. Nadaraya,Nonparametric Density and Regression Estimation [in Russian], Tbilisi Univ. Press, Tbilisi (1983).
I. S. Gradshtein and I. M. Ryzhik,Tables of Integrals Series and Products, Academic Press, New York (1980).
N. S. Bakhvalov,Numerical Methods [in Russian], Nauka, Moscow (1973).
Author information
Authors and Affiliations
Additional information
Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 125–136, Perm, Russia, 1995.
Rights and permissions
About this article
Cite this article
Penskaya, M.Y. Kernel and pseudokernel estimators for the a priori density of a multivariate parameter. J Math Sci 88, 840–847 (1998). https://doi.org/10.1007/BF02365370
Issue Date:
DOI: https://doi.org/10.1007/BF02365370