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Teoriya Veroyatnostei i ee Primeneniya, 1965, Volume 10, Issue 3, Pages 460–478
(Mi tvp542)
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This article is cited in 26 scientific papers (total in 26 papers)
К исследованию асимптотической мощности критериев согласия
D. M. Chibisov Moscow
Abstract:
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].
Received: 21.05.1965
Citation:
D. M. Chibisov, “К исследованию асимптотической мощности критериев согласия”, Teor. Veroyatnost. i Primenen., 10:3 (1965), 460–478; Theory Probab. Appl., 10:3 (1965), 421–437
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