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Journal of Mathematical Sciences

, Volume 127, Issue 1, pp 1723–1736 | Cite as

Detection of a signal of known shape in a multichannel system

  • Yu. I. Ingster
  • I. A. Suslina
Article

Abstract

We consider an n-channel signal detection system. Each of its channels may contain (or not contain) a signal. We assume that the signal is a function of known shape observed in the white Gaussian noise of level ε > 0. Let k be the number of channels containing signals. We study the asymptotically minimax variant of the detection problem as n → ∞ depending on k and on the relation “signal-noise” in the channels. Bibliography: 9 titles.

Keywords

Detection System Gaussian Noise Signal Detection White Gaussian Noise Detection Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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REFERENCES

  1. 1.
    Yu. I. Ingster, “Asymptotically minimax hypothesis testing for nonparametric alternatives. I, II, III, ” Math. Methods Statistics, 2, 85–114, 171-189, 249-268 (1993).Google Scholar
  2. 2.
    Yu. I. Ingster, “Minimax detection of a signal for l n-balls,” Math. Methods Statistics, 7, 401–428 (1998).Google Scholar
  3. 3.
    Yu. I. Ingster, “Adaptive detection of a signal of growing dimension. I,” Math. Methods Statistics, 10, 395–421 (2001).Google Scholar
  4. 4.
    Yu. I. Ingster, “Adaptive detection of a signal of growing dimension. II,” Math. Methods Statistics (2002), to appear.Google Scholar
  5. 5.
    O. V. Lepski, “One problem of adaptive estimation in the Gaussian white noise,” Theory Probab. Appl., 35, 459–470 (1990).Google Scholar
  6. 6.
    O. V. Lepski, “Asymptotic minimax adaptive estimation. 1. Upper bounds,” Theory Probab. Appl., 36, 654–659 (1991).Google Scholar
  7. 7.
    O. V. Lepski, “Asymptotic minimax adaptive estimation. 2. Statistical model without optimal adaptation. Adaptive estimators,” Theory Probab. Appl., 37, 468–481 (1992).Google Scholar
  8. 8.
    V. G. Spokoiny, “Adaptive hypothesis testing using wavelets,” Ann. Stat., 24, 2477–2498 (1996).Google Scholar
  9. 9.
    V. G. Spokoiny, “Adaptive and spatially adaptive testing of nonparametric hypothesis,” Math. Methods Statistics, 7, 245–273 (1998).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Yu. I. Ingster
    • 1
  • I. A. Suslina
    • 2
  1. 1.St. Petersburg State Transport UniversitySt. Petersburg
  2. 2.St.Petersburg State Institute of Fine Mechanics and OpticsSt.Petersburg

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