К исследованию асимптотической мощности критериев согласия

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].