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Problems of Information Transmission

, Volume 53, Issue 3, pp 203–214 | Cite as

Two comparison theorems for distributions of Gaussian quadratic forms

  • M. V. Burnashev
Information Theory
  • 50 Downloads

Abstract

We present new results on comparison of distributions of Gaussian quadratic forms.

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References

  1. 1.
    Bakirov, N.K., Comparison Theorems for Distribution Functions of Quadratic Forms in Gaussian Variables, Teor. Veroyatnost. i Primenen., 1995, vol. 40, no. 2, pp. 404–412 [Theory Probab. Appl. (Engl. Transl.), 1995, vol. 40, no. 2, pp. 340–348].zbMATHMathSciNetGoogle Scholar
  2. 2.
    Wald, A., Statistical Decision Functions, New York: Wiley, 1950. Translated under the title Statisticheskie reshayushchie funktsii, in Pozitsionnye igry (Positional Games), Moscow: Nauka, 1967, pp. 300–522.zbMATHGoogle Scholar
  3. 3.
    Lehmann, E.L., Testing Statistical Hypotheses, New York: Wiley, 1959. Translated under the title Proverka statisticheskikh gipotez, Moscow: Nauka, 1979.zbMATHGoogle Scholar
  4. 4.
    Burnashev, M.V., Minimax Detection of Inaccurately Known Signal in the Background of White Gaussian Noise, Teor. Veroyatnost. i Primenen., 1979, vol. 24, no. 1, pp. 106–118.zbMATHMathSciNetGoogle Scholar
  5. 5.
    Zhang, W. and Poor, H.V., On Minimax Robust Detection of Stationary Gaussian Signals in White Gaussian Noise, IEEE Trans. Inform. Theory, 2011, vol. 57, no. 6, pp. 3915–3924.CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Burnashev, M.V., On Detection of Gaussian Stochastic Sequences, Probl. Peredachi Inform., 2017, in press.Google Scholar
  7. 7.
    Ponomarenko, L.S., Estimation of Distributions of Normal Quadratic Forms of Normally Distributed Random Variables, Teor. Veroyatnost. i Primenen., 1985, vol. 30, no. 3, pp. 545–549.zbMATHMathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2017

Authors and Affiliations

  1. 1.Kharkevich Institute for Information Transmission ProblemsRussian Academy of SciencesMoscowRussia

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