Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 3, pp. 495-509
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V. D. Konakov. Complete asymptotic expansions for the maximum deviation of the empirical density function. Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 3, pp. 495-509. http://geodesic.mathdoc.fr/item/TVP_1978_23_3_a1/
@article{TVP_1978_23_3_a1,
author = {V. D. Konakov},
title = {Complete asymptotic expansions for the maximum deviation of the empirical density function},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {495--509},
year = {1978},
volume = {23},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1978_23_3_a1/}
}
TY - JOUR
AU - V. D. Konakov
TI - Complete asymptotic expansions for the maximum deviation of the empirical density function
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1978
SP - 495
EP - 509
VL - 23
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1978_23_3_a1/
LA - ru
ID - TVP_1978_23_3_a1
ER -
%0 Journal Article
%A V. D. Konakov
%T Complete asymptotic expansions for the maximum deviation of the empirical density function
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1978
%P 495-509
%V 23
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1978_23_3_a1/
%G ru
%F TVP_1978_23_3_a1
Complete asymptotic expansion (19) is obtained for the properly normalized maximum deviation of the empirical density function. As a consequence, the exact rate of convergence to the limiting distribution is found. Some approximations, more useful in practice, and their rates of convergence are also given. In the special histogram case the results obtained are refinements and generalizations of some results of N. V. Smirnov ([5], [7]).
