On the Asymptotic Theory of Statistics of Sequential Ranks

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Previous article Next article On the Asymptotic Theory of Statistics of Sequential RanksA. M. Pardzhanadze and É. V. KhmaladzeA. M. Pardzhanadze and É. V. Khmaladzehttps://doi.org/10.1137/1131089PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. Oosterhoff and , W. Van Zwet, J. Jurechkova, A note on contiguity and Hellinger distanceContributions to Statistics, Reidel, Dordrecht, 1975, 157–166 Google Scholar[2] J. Hajek and , Z. Sidak, Theory of rank tests, Academic Press, New York, 1967, 297– 37:4925 0161.38102 Google Scholar[3] Ole Barndorff-Nielsen, On the limit behaviour of extreme order statistics, Ann. Math. Statist., 34 (1963), 992–1002 27:875 0119.15004 CrossrefGoogle Scholar[4] M. Reynolds, A sequential signed-rank test for symmetry, Ann. Statist., 3 (1975), 382–400 50:11665 0325.62050 CrossrefGoogle Scholar[5] E. V. Khmaladze and , A. M. Parjanadze, Functional limit theorems for linear statistics from sequential ranks, Probab. Theory Related Fields, 73 (1986), 585–595 88m:60098 0584.60044 CrossrefGoogle Scholar[6] P. Bickel and , M. Wichura, Convergence criteria for multiparameter stochastic processes and some applications, Ann. Math. Statist., 42 (1971), 1656–1670 52:4363 0265.60011 CrossrefGoogle Scholar[7] Georg Neuhaus, On weak convergence of stochastic processes with multidimensional time parameter, Ann. Math. Statist., 42 (1971), 1285–1295 45:2783 0222.60013 CrossrefGoogle Scholar[8] I. A. Ibragimov and , R. Z. Khas'minskii, Statistical estimation, Applications of Mathematics, Vol. 16, Springer-Verlag, New York, 1981vii+403, Asymptotic Theory 82g:62006 0467.62026 CrossrefGoogle Scholar[9] Patrick Billingsley, Convergence of probability measures, John Wiley & Sons Inc., New York, 1968xii+253 38:1718 0172.21201 Google Scholar[10] Peter Gaenssler and , Winfried Stute, Empirical processes: a survey of results for independent and identically distributed random variables, Ann. Probab., 7 (1979), 193–243 80d:60002 0402.60031 CrossrefGoogle Scholar[11] Ludger Rüschenforf, Asymptotic distributions of multivariate rank order statistics, Ann. Statist., 4 (1976), 912–923 54:8806 0359.62040 CrossrefGoogle Scholar[12] A. M. Pardzhanadze, Functional limit theorems for a random field constructed from sequential ranks, Summary of Reports of 19th Colloquium on Probability Theory and Mathematical Statistics, Gruz. NIINTI, Tbilisi, 1985, (In Russian.) Google Scholar[13] I. I. Gikhman and , A. V. Skorokhod, The theory of stochastic processes. I, Springer-Verlag, New York, 1974viii+570 49:11603 0291.60019 CrossrefGoogle Scholar[14] David M. Mason, On the use of a statistic based on sequential ranks to prove limit theorems for simple linear rank statistics, Ann. Statist., 9 (1981), 424–436 82h:62033 0459.62015 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails STATISTICAL SIMULATIONS METHOD IN APPLIED STATISTICSIndustrial laboratory. Diagnostics of materials, Vol. 85, No. 5 | 5 June 2019 Cross Ref 20 Weighted sequential empirical type processes with applications to change-point problemsOrder Statistics: Theory & Methods | 1 Jan 1998 Cross Ref The change-point problem for dependent observationsJournal of Statistical Planning and Inference, Vol. 53, No. 3 | 1 Aug 1996 Cross Ref Linear rank statistics, finite sampling, permutation tests and WinsorizingThe Annals of Statistics, Vol. 24, No. 3 | 1 Jun 1996 Cross Ref Weak convergence of weighted empirical type processes under contiguous and changepoint alternativesStochastic Processes and their Applications, Vol. 50, No. 2 | 1 Apr 1994 Cross Ref The Chibisov—O'Reilly theorem for empirical processes under contiguous measuresStatistics & Probability Letters, Vol. 19, No. 2 | 1 Jan 1994 Cross Ref Volume 31, Issue 4| 1987Theory of Probability & Its Applications563-742 History Submitted:04 November 1985Published online:17 July 2006 InformationCopyright © 1987 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1131089Article page range:pp. 669-682ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics