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Probl. Peredachi Inf., 1998, Volume 34, Issue 1, Pages 56–68 (Mi ppi395)  

This article is cited in 5 scientific papers (total in 6 papers)

Methods of Signal Processing

Minimax Detection of a Signal for Besov Bodies and Balls

Yu. I. Ingster, I. A. Suslina


Abstract: We consider an asymptotical minimax problem of detection of a signal from functional sets corresponding to the Besov balls $B^\sigma_{p,q}(C)$ or Besov bodies $\Theta^s_{p,q}(C)$ with a remote $L_2$-ball, the signal being observed in the Gaussian white noise of intensity $\varepsilon>0$, $\sigma>0$, $s=\sigma-1/p+1/2>0$. For the case of Besov bodies, for $q\geq p$ or $\min(p,q)\geq 2$, asymptotically exact estimates of the minimax probability of the detection errors are obtained, while for other cases and Besov balls, asymptotically exact conditions of the minimax distinguishability are found.

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English version:
Problems of Information Transmission, 1998, 34:1, 48–59

Bibliographic databases:

UDC: 621.391.1
Received: 09.10.1995
Revised: 17.11.1997

Citation: Yu. I. Ingster, I. A. Suslina, “Minimax Detection of a Signal for Besov Bodies and Balls”, Probl. Peredachi Inf., 34:1 (1998), 56–68; Problems Inform. Transmission, 34:1 (1998), 48–59

Citation in format AMSBIB
\Bibitem{IngSus98}
\by Yu.~I.~Ingster, I.~A.~Suslina
\paper Minimax Detection of a~Signal for Besov Bodies and Balls
\jour Probl. Peredachi Inf.
\yr 1998
\vol 34
\issue 1
\pages 56--68
\mathnet{http://mi.mathnet.ru/ppi395}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1654822}
\zmath{https://zbmath.org/?q=an:1113.94303}
\transl
\jour Problems Inform. Transmission
\yr 1998
\vol 34
\issue 1
\pages 48--59


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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. Sylvestre, J, “Time-frequency detection algorithm for gravitational wave bursts”, Physical Review D, 66:10 (2002), 102004  crossref  adsnasa  isi
    2. Baraud, Y, “Non-asymptotic minimax rates of testing in signal detection”, Bernoulli, 8:5 (2002), 577  mathscinet  zmath  isi
    3. Baraud, Y, “Adaptive tests of linear hypotheses by model selection”, Annals of Statistics, 31:1 (2003), 225  crossref  mathscinet  zmath  isi
    4. Laurent B., Loubes J.-M., Marteau C., “Non Asymptotic Minimax Rates of Testing in Signal Detection with Heterogeneous Variances”, Electron. J. Stat., 6 (2012), 91–122  crossref  mathscinet  zmath  isi  elib
    5. “To the memory of Yu. I. Ingster”, J. Math. Sci. (N. Y.), 204:1 (2015), 1–6  mathnet  crossref  mathscinet
    6. Blanchard G., Carpentier A., Gutzeit M., “Minimax Euclidean Separation Rates For Testing Convex Hypotheses in R-D”, Electron. J. Stat., 12:2 (2018), 3713–3735  crossref  mathscinet  zmath  isi  scopus
  • Проблемы передачи информации Problems of Information Transmission
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