Abstract:
This paper is a continuation of author's paper [I]. Like [I] we consider here a sample (x1,…,xn) with common density f(x−Θ) depending on unknown parameter Θ. It is supposed that f is sufficiently
smooth exept the finite set of points of singularity of the form (1.1).
The main result asserts that for Bayesian estimates ^tn random variables n1/1+α(^tn−Θ) has a proper limit distribution where α is from (1.1).
Citation:
I. A. Ibragimov, R. Z. Khas'minskii, “Asymptotic behavior of statistical estimates of the shift parameter for samples with unbounded density”, Problems of the theory of probability distributions. Part 3, Zap. Nauchn. Sem. LOMI, 55, "Nauka", Leningrad. Otdel., Leningrad, 1976, 175–184; J. Soviet Math., 16:2 (1981), 1035–1041
\Bibitem{IbrKha76}
\by I.~A.~Ibragimov, R.~Z.~Khas'minskii
\paper Asymptotic behavior of statistical estimates of the shift parameter for samples with unbounded density
\inbook Problems of the theory of probability distributions. Part~3
\serial Zap. Nauchn. Sem. LOMI
\yr 1976
\vol 55
\pages 175--184
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl2848}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=413338}
\zmath{https://zbmath.org/?q=an:0361.62025|0486.62035}
\transl
\jour J. Soviet Math.
\yr 1981
\vol 16
\issue 2
\pages 1035--1041
\crossref{https://doi.org/10.1007/BF01676146}
Linking options:
https://www.mathnet.ru/eng/znsl2848
https://www.mathnet.ru/eng/znsl/v55/p175
This publication is cited in the following 5 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
Thanakorn Nitithumbundit, Jennifer S. K. Chan, “Maximum leave-one-out likelihood method for the location parameter of variance gamma distribution with unbounded density”, Journal of Statistical Computation and Simulation, 93:15 (2023), 2642
Thanakorn Nitithumbundit, Jennifer S.K. Chan, “ECM algorithm for estimating vector ARMA model with variance gamma distribution and possible unbounded density”, Aus NZ J of Statistics, 63:3 (2021), 485
Krzysztof Podgórski, Jonas Wallin, “Maximizing leave-one-out likelihood for the location parameter of unbounded densities”, Ann Inst Stat Math, 67:1 (2015), 19
M. S. Ermakov, “Asymptotic behavior of statistical estimates of parameters for multidimensional discontinuities density”, J. Soviet Math., 34:1 (1986), 1413–1427
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