К исследованию асимптотической мощности критериев согласия
Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 3, pp. 460-478
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Let $G_n^*(u)$ be the empirical distribution function of a sample of size $n$ from a distribution function $G(u)$, $0\le u\le1$, and $\beta_n(u)=\sqrt n(G_n^*(u)-u)$. It is proved, that if $G(u)=G_n(u)$ and $\sqrt n(G_n(u)-u)\to\delta(u)$ as $n\to\infty$, $\beta_n(u)$ converges to $\beta(u)+\delta(u)$ where $\beta(u)$ is the gaussian process with $\mathbf M\beta(u)=0$, $\mathbf M\beta(u)\beta(v)=\min(u,v)-uv$. The exact meanings of convergence are indicated in the statements of theorems. The results of this paper were published without proofs in [6].
@article{TVP_1965_10_3_a4,
author = {D. M. Chibisov},
title = {{\CYRK} {\cyri}{\cyrs}{\cyrs}{\cyrl}{\cyre}{\cyrd}{\cyro}{\cyrv}{\cyra}{\cyrn}{\cyri}{\cyryu} {\cyra}{\cyrs}{\cyri}{\cyrm}{\cyrp}{\cyrt}{\cyro}{\cyrt}{\cyri}{\cyrch}{\cyre}{\cyrs}{\cyrk}{\cyro}{\cyrishrt} {\cyrm}{\cyro}{\cyrshch}{\cyrn}{\cyro}{\cyrs}{\cyrt}{\cyri} {\cyrk}{\cyrr}{\cyri}{\cyrt}{\cyre}{\cyrr}{\cyri}{\cyre}{\cyrv} {\cyrs}{\cyro}{\cyrg}{\cyrl}{\cyra}{\cyrs}{\cyri}{\cyrya}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {460--478},
publisher = {mathdoc},
volume = {10},
number = {3},
year = {1965},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a4/}
}
D. M. Chibisov. К исследованию асимптотической мощности критериев согласия. Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 3, pp. 460-478. http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a4/