This is a preview of subscription content, log in via an institution to check access.
Literature cited
M. Ya. Penskaya, “Estimation of an a priori distribution density,”Probl. Ustoich. Stokh. Mod., 112–119 (1984).
G. G. Walter, “Integral equation estimation of the prior distribution,”Sankhya,A46, No. 1, 75–84 (1984).
I. E. Simonova, “Application of the method of regularization to the estimation of distributions,”Zh. Vychisl. Mat i Mat Fit.,22, No. 4 (1982).
A. V. Goncharskii, A. S. Leonov, and A. G. Yagola, “On regularization of ill-posed problems with an approximately known operator,”Zh. Vychisl. Mat. i Mat. Fiz.,14, No. 4, 1022–1027 (1974).
N. B. Zyabrev and T. I. Savelova, “On estimating the rate of convergence of regularized solutions of an equation of convolution type with errors in the kernel and right-hand side,”Zh. Vychisl. Mat. i Mat. Fiz.,16, No. 5, 1091–1101 (1976).
T. I. Savelova, “On the optimal regularization of equations of convolution type with random noise in the kernel and right-hand side,”Zh. Vychisl. Mat. i Mat. Fiz.,18, No. 2, 275–283 (1978).
A. N. Tikhonov and V. Ya. Arsenin,Methods of Solving Ill-posed Problems [in Russian], Nauka, Moscow (1979).
I. E. Simonova, “On direct and inverse problems of estimating functionals of distribution functions,”Stat Met., Perm' Univ., 125–133 (1982).
M. Ya. Penskaya, “Application of regularizing operators in the theory of statistical estimation,”Stat. Met. Otsen. i Prov. Gipot., Perm' Univ., 158–166 (1986).
V. N. Vapnik,Estimation of Dependences based on Empirical Data, Springer, New York (1982).
Additional information
Translated from:Problemy Ustoichivosti Stokhasticheskikh Modelei, Trudy Seminara, 1989, pp. 125–130.
Rights and permissions
About this article
Cite this article
Penskaya, M.Y. Stable estimation of an a priori density. J Math Sci 59, 992–996 (1992). https://doi.org/10.1007/BF01099130
Issue Date:
DOI: https://doi.org/10.1007/BF01099130