On the Rate of Convergence to the Normal Law of Finitely Truncated Linear Combinations of Order Statistics

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Previous article Next article On the Rate of Convergence to the Normal Law of Finitely Truncated Linear Combinations of Order StatisticsN. V. GribkovaN. V. Gribkovahttps://doi.org/10.1137/1133111PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Steinar Bjerve, Error bounds for linear combinations of order statistics, Ann. Statist., 5 (1977), 357–369 58:24666 0356.62015 CrossrefGoogle Scholar[2] R. Helmers, A Berry-Esseen theorem for linear combinations of order statistics, Ann. Probab., 9 (1981), 342–347 82i:62074 0474.62039 CrossrefGoogle Scholar[3] R. Helmers, Edgeworth expansions for linear combinations of order statistics, Mathematical Centre Tracts, Vol. 105, Mathematisch Centrum, Amsterdam, 1982iv+137 84f:62029 0485.62017 Google Scholar[4] V. A. Egorov and , V. B. Nevzorov, Certain estimates of the rate of convergence of sums of order statistics to the normal law, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 41 (1974), 105–128, 167, (In Russian.) 51:2148 Google Scholar[5] N. V. Gribkova, An estimate for the rate of convergence to the normal law of truncated linear combinations of order statistics, Mat. Zametki, 42 (1987), 739–746, 764, (In Russian.) 89b:60056 0634.62016 Google Scholar[6] W. R. van Zwet, A Berry-Esseen bound for symmetric statistics, Z. Wahrsch. Verw. Gebiete, 66 (1984), 425–440 86h:60063 0525.62023 CrossrefGoogle Scholar[7] H. A. David, Order statistics, John Wiley & Sons Inc., New York, 1970xi+272 44:3440 0223.62057 Google Scholar[8] Stephen M. Stigler, Linear functions of order statistics with smooth weight functions, Ann. Statist., 2 (1974), 676–693 51:9354 0286.62028 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Volume 33, Issue 4| 1989Theory of Probability & Its Applications595-765 History Submitted:16 March 1987Published online:28 July 2006 InformationCopyright © 1988 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1133111Article page range:pp. 726-729ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics