Problems of Information Transmission

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

Two comparison theorems for distributions of Gaussian quadratic forms

Information Theory


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


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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].MATHMathSciNetGoogle 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.MATHGoogle Scholar
  3. 3.
    Lehmann, E.L., Testing Statistical Hypotheses, New York: Wiley, 1959. Translated under the title Proverka statisticheskikh gipotez, Moscow: Nauka, 1979.MATHGoogle 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.MATHMathSciNetGoogle 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.CrossRefMATHMathSciNetGoogle 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.MATHMathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2017

Authors and Affiliations

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

Personalised recommendations