Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part 3, Tome 55 (1976), pp. 175-184
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I. A. Ibragimov; R. Z. Khas'minskii. Asymptotic behavior of statistical estimates of the shift parameter for samples with unbounded density. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part 3, Tome 55 (1976), pp. 175-184. http://geodesic.mathdoc.fr/item/ZNSL_1976_55_a10/
@article{ZNSL_1976_55_a10,
author = {I. A. Ibragimov and R. Z. Khas'minskii},
title = {Asymptotic behavior of statistical estimates of the shift parameter for samples with unbounded density},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {175--184},
year = {1976},
volume = {55},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_55_a10/}
}
TY - JOUR
AU - I. A. Ibragimov
AU - R. Z. Khas'minskii
TI - Asymptotic behavior of statistical estimates of the shift parameter for samples with unbounded density
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1976
SP - 175
EP - 184
VL - 55
UR - http://geodesic.mathdoc.fr/item/ZNSL_1976_55_a10/
LA - ru
ID - ZNSL_1976_55_a10
ER -
%0 Journal Article
%A I. A. Ibragimov
%A R. Z. Khas'minskii
%T Asymptotic behavior of statistical estimates of the shift parameter for samples with unbounded density
%J Zapiski Nauchnykh Seminarov POMI
%D 1976
%P 175-184
%V 55
%U http://geodesic.mathdoc.fr/item/ZNSL_1976_55_a10/
%G ru
%F ZNSL_1976_55_a10
This paper is a continuation of author's paper [I]. Like [I] we consider here a sample $(x_1,\dots,x_n)$ with common density $f(x-\Theta)$ depending on unknown parameter $\Theta$. 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 $\hat{t}_n$ random variables $n^{1/1+\alpha}(\hat{t}_n-\Theta)$ has a proper limit distribution where $\alpha$ is from (1.1).
