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Teor. Veroyatnost. i Primenen., 1964, Volume 9, Issue 3, Pages 561–562 (Mi tvp407)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

On the Asymptotic Power of the Tests of Fit by Near Alternatives

D. M. Čibisov

Moscow

Abstract: 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.

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English version:
Theory of Probability and its Applications, 1964, 9:3, 507–508

Bibliographic databases:

Received: 01.06.1964

Citation: D. M. Čibisov, “On the Asymptotic Power of the Tests of Fit by Near Alternatives”, Teor. Veroyatnost. i Primenen., 9:3 (1964), 561–562; Theory Probab. Appl., 9:3 (1964), 507–508

Citation in format AMSBIB
\Bibitem{Chi64}
\by D.~M.~{\v C}ibisov
\paper On the Asymptotic Power of the Tests of Fit by Near Alternatives
\jour Teor. Veroyatnost. i Primenen.
\yr 1964
\vol 9
\issue 3
\pages 561--562
\mathnet{http://mi.mathnet.ru/tvp407}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=166882}
\zmath{https://zbmath.org/?q=an:0132.13505}
\transl
\jour Theory Probab. Appl.
\yr 1964
\vol 9
\issue 3
\pages 507--508
\crossref{https://doi.org/10.1137/1109072}


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    This publication is cited in the following articles:
    1. J. Appl. Industr. Math., 3:4 (2009), 462–475  mathnet  crossref  mathscinet
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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