Martingale Limit Theorems for Divisible Statistics

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Previous article Next article Martingale Limit Theorems for Divisible StatisticsE. V. KhmaladzeE. V. Khmaladzehttps://doi.org/10.1137/1128049PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Yu. I. Medvedev, Some theorems on the asymptotic distribution of the $\chi \sp{2}$ statistic, Dokl. Akad. Nauk SSSR, 192 (1970), 987–989, (In Russian.) 42:1263 Google Scholar[2] V. F. Kolchin, , B. A. Sevast'yanov and , V. P. Chistyakov, Random allocations, V. H. Winston & Sons, Washington, D.C., 1978xi+262 57:10758b Google Scholar[3] Yu. K. Orlov and , R. Ya. Chitashlivi, On the statistical significance of the Zipf laws, Soobshcheniya AN GrSSR, 108 (1982), 513–516, (In Russian.) Google Scholar[4] Yu. I. Medvedev, Separable statistics in a polynomial scheme, I, II, Theory Prob. Appl., 22 (1977), 1–15, 22 (1977), pp. 607–615 LinkGoogle Scholar[5] G. I. Ivchenko and , Yu. I. Medvedev, Decomposable statistics and hypothesis testing for grouped data, Theory Prob. Appl., 25 (1980), 540–551 0494.62052 LinkGoogle Scholar[6] C. Morris, Central limit theorems for multinomial sums, Ann. Statist., 3 (1975), 165–188 51:7094 0305.62013 CrossrefGoogle Scholar[7] R. Sh. Liptser and , A. N. Shiryaev, The functional central limit theorem f or semi-martingaless, Theory Prob. Appl., 25 (1980), 680–703 Google Scholar[8] P. Billingsley, Convergence of probability measures, John Wiley & Sons Inc., New York, 1968xii+253 38:1718 0172.21201 Google Scholar[9] R. Sh. Liptser and , A. N. Shiryaev, Statistics of Random Processes, Springer, New York, 1977–78 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails The probabilities of large deviations for a certain class of statistics associated with multinomial distribution9 October 2020 | ESAIM: Probability and Statistics, Vol. 24 Cross Ref A Conversation with Estate V. KhmaladzeStatistical Science, Vol. 31, No. 3 Cross Ref Convergence Properties in Certain Occupancy Problems Including the Karlin-Rouault Law14 July 2016 | Journal of Applied Probability, Vol. 48, No. 4 Cross Ref Martingale limit theorems of divisible statistics in a multinomial scheme with mixed frequenciesStatistics & Probability Letters, Vol. 81, No. 8 Cross Ref Estimation of Functionals of a DensityV. P. Borovikov17 July 2006 | Theory of Probability & Its Applications, Vol. 37, No. 3AbstractPDF (543 KB)Tests of Homogeneity under Small Grouping. Martingale Limit TheoremsI. K. Urinov17 July 2006 | Theory of Probability & Its Applications, Vol. 37, No. 4AbstractPDF (1268 KB)Goodness-of-Fit Tests for Generalized Urn Schemes Based on Separable StatisticsA. F. Ronzhin17 July 2006 | Theory of Probability & Its Applications, Vol. 33, No. 1AbstractPDF (980 KB)Limit Theorems for Statistics that are Partial Sums of Functions of SpacingsV. P. Borovikov17 July 2006 | Theory of Probability & Its Applications, Vol. 32, No. 1AbstractPDF (904 KB)On the Convergence of Separable Statistics to a Wiener ProcessR. M. Mnatsakanov17 July 2006 | Theory of Probability & Its Applications, Vol. 32, No. 1AbstractPDF (438 KB)On the Convergence of Divisible Statistics to the Poisson ProcessR. M. Mnatsakanov17 July 2006 | Theory of Probability & Its Applications, Vol. 32, No. 2AbstractPDF (537 KB)On a Method for Constructing Goodness-of-Fit Tests for Parametric Hypotheses in $R^m$A. M. Nikabadze17 July 2006 | Theory of Probability & Its Applications, Vol. 32, No. 3AbstractPDF (498 KB)A Functional Limit Theorem for Additively Separable Statistics in the Case of Very Rare EventsR. M. Mnatsakanov17 July 2006 | Theory of Probability & Its Applications, Vol. 30, No. 3AbstractPDF (424 KB)Estimates of Closeness of the Distribution of a Randomized Separable Statistic to the Normal Law in a Multinomial SchemeSh. A. Mirakhmedov28 July 2006 | Theory of Probability & Its Applications, Vol. 30, No. 1AbstractPDF (472 KB) Volume 28, Issue 3| 1984Theory of Probability & Its Applications History Submitted:14 April 1982Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1128049Article page range:pp. 530-548ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics