Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 1, pp. 78-93
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I. A. Ibragimov; R. Z. Khas'minskii. Asymptotical behaviour of some statistical estimators. II. Limiting theorems for the a posteriory density and Bayesian estimators. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 1, pp. 78-93. http://geodesic.mathdoc.fr/item/TVP_1973_18_1_a5/
@article{TVP_1973_18_1_a5,
author = {I. A. Ibragimov and R. Z. Khas'minskii},
title = {Asymptotical behaviour of some statistical estimators. {II.~Limiting} theorems for the a posteriory density and {Bayesian} estimators},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {78--93},
year = {1973},
volume = {18},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_1_a5/}
}
TY - JOUR
AU - I. A. Ibragimov
AU - R. Z. Khas'minskii
TI - Asymptotical behaviour of some statistical estimators. II. Limiting theorems for the a posteriory density and Bayesian estimators
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1973
SP - 78
EP - 93
VL - 18
IS - 1
UR - http://geodesic.mathdoc.fr/item/TVP_1973_18_1_a5/
LA - ru
ID - TVP_1973_18_1_a5
ER -
%0 Journal Article
%A I. A. Ibragimov
%A R. Z. Khas'minskii
%T Asymptotical behaviour of some statistical estimators. II. Limiting theorems for the a posteriory density and Bayesian estimators
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1973
%P 78-93
%V 18
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1973_18_1_a5/
%G ru
%F TVP_1973_18_1_a5
In the second part of the paper we use propositions, methods and results of the first part appeared in the previous issue of this journal. Under conditions I–IV of § 1, we prove theorems about behaviour of the a posteriory density (similar to the well-known Le Cam's results [2]), Bayesian estimators $t_n^{(a)}$ for the risk function $\|\theta\|^a$, Pitman's estimators of the location parameter etc. We prove, for example, that the estimators $t_n^{(a)}$, for different $a\ge1$, are equivalent in the sense that $$ \mathbf E\{\sqrt n\bigl|t_n^{(a_1)}-t_n^{(a_2)}\bigr|\}^p\underset{n\to\infty}\longrightarrow0\quad(p>0). $$
