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Teor. Veroyatnost. i Primenen., 1965, Volume 10, Issue 3, Pages 460–478 (Mi tvp542)  

This article is cited in 5 scientific papers (total in 5 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].

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English version:
Theory of Probability and its Applications, 1965, 10:3, 421–437

Bibliographic databases:

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

Citation in format AMSBIB
\Bibitem{Chi65}
\by D.~M.~Chibisov
\paper К исследованию асимптотической мощности критериев согласия
\jour Teor. Veroyatnost. i Primenen.
\yr 1965
\vol 10
\issue 3
\pages 460--478
\mathnet{http://mi.mathnet.ru/tvp542}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=191025}
\zmath{https://zbmath.org/?q=an:0139.37302}
\transl
\jour Theory Probab. Appl.
\yr 1965
\vol 10
\issue 3
\pages 421--437
\crossref{https://doi.org/10.1137/1110050}


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    Citing articles on Google Scholar: Russian citations, English citations
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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
    2. Makhoukhi M.B., “An approximation for the power function of a non–parametric test of fit”, Statistics & Probability Letters, 78:8 (2008), 1034–1042  crossref  mathscinet  isi
    3. “An extended continous mapping theorem for outer almost sure weak convergence”, Theory Probab. Appl., 64:2 (2019), 304–323  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. M. V. Boldin, “Local power of Kolmogorov’s and omega-squared type criteria in autoregression”, Moscow University Mathematics Bulletin, 74:6 (2019), 249–252  mathnet  crossref  isi
    5. M. S. Ermakov, “O ravnomernoi sostoyatelnosti neparametricheskikh kriteriev. I”, Veroyatnost i statistika. 28, Zap. nauchn. sem. POMI, 486, POMI, SPb., 2019, 98–147  mathnet
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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