Distinguishing Neighboring Hypotheses About Frequency Distributions in the Scheme of the Generalized Probability Ratio Test
S. A. Aivazyan · Theory of Probability and Its Applications · 1965
Previous article Next article Distinguishing Neighboring Hypotheses About Frequency Distributions in the Scheme of the Generalized Probability Ratio TestS. A. AivazyanS. A. Aivazyanhttps://doi.org/10.1137/1110078PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] S. A. Ai˘vazjan, Comparison of the optimal properties of the Wald and Neyman-Pearson criteria, Theor. Probability Appl., 4 (1959), 83–89, (English translation.) MR0121905 LinkGoogle Scholar[2] L. N. Bol'šev and , N. V. Smirnov, Tablitsy matematicheskoi statistiki, Izdat. “Nauka”, Moscow, 1965, 464– MR0182072 Google Scholar[3] Abraham Wald, Sequential Analysis, John Wiley & Sons Inc., New York, 1947xii+212 MR0020764 0029.15805 Google Scholar[4] E. L. Lehmann, Testing statistical hypotheses, John Wiley & Sons Inc., New York, 1959xiii+369 MR0107933 0089.14102 Google Scholar[5] V. M. Zolotarev, The first passage time of a level and the behavior at infinity for a class of processes with independent increments, Theory Prob. Applications, 9 (1964), 653–662, (English translation.) 10.1137/1109090 LinkGoogle Scholar[6] Yu. V. Prokhorov, Convergence of random processes and limit theorems in probability theory, Theory Prob. Applications, 1 (1956), 157–214, (English translation.) 10.1137/1101016 LinkGoogle Scholar[7] T. W. Anderson, The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities, Proc. Amer. Math. Soc., 6 (1955), 170–176 MR0069229 0066.37402 CrossrefGoogle Scholar[8] T. W. Anderson, A modification of the sequential probability ratio test to reduce the sample size, Ann. Math. Statist., 31 (1960), 165–197 MR0116441 0089.35501 CrossrefGoogle Scholar[9] D. A. Darling and , A. J. F. Siegert, The first passage problem for a continuous Markov process, Ann. Math. Statistics, 24 (1953), 624–639 MR0058908 0053.27301 CrossrefGoogle Scholar[10] Wassily Hoeffding, Lower bounds for the expected sample size and the average risk of a sequential procedure, Ann. Math. Statist., 31 (1960), 352–368 MR0120750 0098.32705 CrossrefGoogle Scholar[11] J. Kiefer and , Lionel Weiss, Some properties of generalized sequential probability ratio tests, Ann. Math. Statist., 28 (1957), 57–74 MR0087290 0079.35406 CrossrefGoogle Scholar[12] S. Kullback and , R. A. Leibler, On information and sufficiency, Ann. Math. Statistics, 22 (1951), 79–86 MR0039968 0042.38403 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails High-Performance Sequential Analysis in Grid Automated Systems of Distributed-Generation Areas5 May 2021 | Russian Electrical Engineering, Vol. 92, No. 2 Cross Ref Application of the Wald Sequential Procedure in Automatic Network Control with Distributed Generation15 December 2020 Cross Ref About the Effectiveness of the Statistical Sequential Analysis in the Reliability Trials Cross Ref Volume 10, Issue 4| 1965Theory of Probability & Its Applications History Submitted:04 August 1965Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1110078Article page range:pp. 646-658ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics