Abstract
We study the asymptotic behavior of Bayesian and maximum likelihood estimators of the parameter θ when the density function f(x, θ) for each fixed x has discontinuities in θ on some surface.
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Literature cited
I. A. Ibragimov and R. Z. Khas'minskii, “Asymptotic behavior of estimators for samples with discontinuous density,” Mat. Sb.,87(129), No. 4, 554–586 (1972).
I. A. Ibragimov and R. Z. Khas'minskii, “Asymptotic behavior of some estimators in the smooth case. I,” Teor. Veroyatn. Primen.,17, No. 3, 469–486 (1972).
I. A. Ibragimov and R. Z. Khas'minskii, “Asymptotic behavior of some estimators in the smooth case. II,” Teor. Veroyatn. Primen.,18, No. 1, 78–93 (1973).
I. A. Ibragimov and R. Z. Khas'minskii, “On moments of generalized Bayesian estimators and maximum likelihood estimators,” Teor. Veroyatn. Primen.,18, No. 3, 535–546 (1973).
I. A. Ibragimov and R. Z. Khas'minskii, “Asymptotic behavior of location parameter estimators for samples with unbounded density,” J. Sov. Math.,16, No. 2 (1981).
I. A. Ibragimov and R. Z. Khas'minskii, “On sequential estimation of the location parameter for samples with discontinuous density,” Teor. Veroyatn. Primen.,19, No. 4, 700–717 (1974).
H. Rubin, “The estimation of discontinuities in multivariate densities and related problems in stochastic processes,” Proc. 4th Berkeley Symp. on Prob. Theory and Statistics, Vol. 1 (1961), pp. 563–574.
I. I. Gikhman and A. V. Skorokhod, An Introduction to the Theory of Random Processes [in Russian], Nauka, Moscow (1965).
A. A. Borovkov, “Convergence of distributions of functionals of stochastic processes,” Usp. Mat. Nauk,27, No. 1(163), 3–41 (1972).
P. J. Bickel and J. A. Yahav, “Asymptotically optimal Bayes and minimax procedures in sequential estimation,” AMS,39, 442–456 (1968).
M. S. Ermakov, “On asymptotic behavior of estimators for samples having densities with singularities,” Teor. Veroyatn. Primen.,21, No. 3, 666–668 (1976).
I. A. Ibragimov and R. Z. Khas'minskii, “On sequential estimation,” Teor. Veroyatn. Primen.,19, No. 2, 245–256 (1974).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 74, pp. 83–107, 1977.
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Ermakov, M.S. Asymptotic behavior of parameter estimators of a multivariate discontinuous density. J Math Sci 34, 1413–1427 (1986). https://doi.org/10.1007/BF01085009
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DOI: https://doi.org/10.1007/BF01085009