Geodesic
On the Asymptotic Power of the Tests of Fit by Near Alternatives
Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 3, pp. 561-562 
D. M. Čibisov. On the Asymptotic Power of the Tests of Fit by Near Alternatives. Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 3, pp. 561-562. http://geodesic.mathdoc.fr/item/TVP_1964_9_3_a17/
@article{TVP_1964_9_3_a17,
     author = {D. M. \v{C}ibisov},
     title = {On the {Asymptotic} {Power} of the {Tests} of {Fit} by {Near} {Alternatives}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {561--562},
     year = {1964},
     volume = {9},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1964_9_3_a17/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $G_n^*(u)$ be the empirical distribution of a sample of size $n$ from a distribution function $G(u)$, $0 \leqq u\leqq 1$, 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 definitions of convergence are indicated in the statements of theorems.