On a Problem of Signal Detection Leading to Stable Distributions
Marat Valievich Burnashev, I. A. Begmatov · Theory of Probability and Its Applications · 1991
Previous article Next article On a Problem of Signal Detection Leading to Stable DistributionsM. V. Burnashev and I. A. BegmatovM. V. Burnashev and I. A. Begmatovhttps://doi.org/10.1137/1135076PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. S. Liptzer and , A. N. Shiryaev, Statistics of random processes. I, Springer-Verlag, New York, 1977x+394, Berlin 57:14125 0364.60004 CrossrefGoogle Scholar[2] I. A. Ibragimov and , R. Z. Khas'minskii, Statistical Estimation; Asymptotic Theory, Applications of Mathematics, Vol. 16, Springer-Verlag, New York, 1981vii+403, Berlin, Heidelberg 82g:62006 0467.62026 CrossrefGoogle Scholar[3] M. V. Burnashev, On the minimax detection of an inaccurately known signal in a white Gaussian noise background, Theory Probab. Appl., 24 (1979), 107–119 10.1137/1124008 0433.60043 LinkGoogle Scholar[4] P. A. Bakuta, Theory of Signal Detection, Radio and Communication, Moscow, 1984 Google Scholar[5] M. V. Burnashev, On a statistical problem related to random walks, Theory Probab. Appl., 26 (1981), 554–563 10.1137/1126060 0499.62071 LinkGoogle Scholar[6] R. L. Dobrushin, A statistical problem arising in the theory of detection of signal in the presence of noise in a multichannel system and leading to stable distribution laws, Theory Probab. Appl., 3 (1958), 161–173 10.1137/1103015 0116.35105 LinkGoogle Scholar[7] H. Urkowitz, Energy detection of unknown deterministic signals, Proc. IEEE, 55 (1967), 523–531 CrossrefGoogle Scholar[8] N. F. Krasner, Efficient search methods using energy detectors—maximum probability of detection, IEEE J. Select. Areas Comm., SAC-4 (1986), 273–279 10.1109/JSAC.1986.1146316 CrossrefGoogle Scholar[9] A. Wald, Statistical Decision Functions, Games, Nauka, Moscow, 1967, 300–522, (In Russian.) Google Scholar[10] J. R. Barra, Notions fondamentales de statistique mathématique, Dunod, Paris, 1971xix+258 53:6805 0257.62004 Google Scholar[11] V. V. Petrov, Limit Theorems for Sums of Independent Random Variables, Nauka, Moscow, 1987, (In Russian.) 0621.60022 Google Scholar[12] R. Gallagher, Information Theory and Reliable Communication, Springer-Verlag, Vienna, New York, 1972 CrossrefGoogle Scholar[13] I. A. Ibragimov, , A. S. Nemirovskh and , R. Z. Khas'minskh, Some problems on nonparametric estimation in Gaussian white noise, Theory Probab. Appl., 31 (1986), 391–406 10.1137/1131054 0623.62028 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails MAP and Bayes tests in sparse vectors detection8 March 2022 | Statistical Inference for Stochastic Processes, Vol. 52 Cross Ref Multi-level Bayes and MAP Monotonicity Testing31 August 2021 | Mathematical Methods of Statistics, Vol. 29, No. 1 Cross Ref Optimal Detection of Sparse Mixtures Against a Given Null DistributionIEEE Transactions on Information Theory, Vol. 60, No. 4 Cross Ref Optimal detection of heterogeneous and heteroscedastic mixtures9 August 2011 | Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 73, No. 5 Cross Ref Near-Optimal Detection of Geometric Objects by Fast Multiscale MethodsIEEE Transactions on Information Theory, Vol. 51, No. 7 Cross Ref On identification capacity of infinite alphabets or continuous-time channelsIEEE Transactions on Information Theory, Vol. 46, No. 7 Cross Ref Volume 35, Issue 3| 1991Theory of Probability & Its Applications History Submitted:08 February 1988Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1135076Article page range:pp. 556-560ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics