Abstract:
In this paper the authors study the asymptotic behavior of the joint distribution and moments of generalized Bayesian estimates, maximum likelihood estimates and maximum probability estimates with respect to intervals constructed from independent observations with a density having a discontinuity of the first kind.
Bibliography: 9 titles.
Citation:
I. A. Ibragimov, R. Z. Khas'minskii, “Asymptotic behavior of statistical estimates for samples with a discontinuous density”, Math. USSR-Sb., 16:4 (1972), 573–606
\Bibitem{IbrKha72}
\by I.~A.~Ibragimov, R.~Z.~Khas'minskii
\paper Asymptotic behavior of statistical estimates for samples with a~discon\-tinuous density
\jour Math. USSR-Sb.
\yr 1972
\vol 16
\issue 4
\pages 573--606
\mathnet{http://mi.mathnet.ru/eng/sm3140}
\crossref{https://doi.org/10.1070/SM1972v016n04ABEH001440}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=301852}
\zmath{https://zbmath.org/?q=an:0297.62022}
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https://doi.org/10.1070/SM1972v016n04ABEH001440
https://www.mathnet.ru/eng/sm/v129/i4/p554
This publication is cited in the following 6 articles:
A. A. Borovkov, Al. V. Bulinski, A. M. Vershik, D. Zaporozhets, A. S. Holevo, A. N. Shiryaev, “Ildar Abdullovich Ibragimov (on his ninetieth birthday)”, Russian Math. Surveys, 78:3 (2023), 573–583
Alexander Gushchin, Nino Kordzakhia, Alexander Novikov, “Translation invariant statistical experiments with independent increments”, Stat. Inference Stoch. Process., 21:2 (2018), 363–383
O. V. Chernoyarov, Yu. A. Kutoyants, A. Top, “On multiple change-point estimation for Poisson process”, Communications in Statistics - Theory and Methods, 47:5 (2018), 1215
Georg Ch. Pflug, “The limiting log-likelihood process for discontinuous density families”, Z. Wahrscheinlichkeitstheorie verw Gebiete, 64:1 (1983), 15
Wilfried Grossmann, Lecture Notes in Statistics, 8, The First Pannonian Symposium on Mathematical Statistics, 1981, 94
N. K. Bakirov, “Likelihood ratio for densities with singularity”, J. Soviet Math., 34:1 (1986), 1403–1413
Citation in format AMSBIB
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