On an Estimate of the Remainder Term in the Central Limit Theorem

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Previous article Next article On an Estimate of the Remainder Term in the Central Limit TheoremL. V. Osipov and V. V. PetrovL. V. Osipov and V. V. Petrovhttps://doi.org/10.1137/1112030PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. Bikyalis, Limit theorems for sums of independent random vectors, 1965, Author's report on his dissertation, Vil'nus Google Scholar[2] A. Bikyalis, Estimates for the remainder term in the central limit theorem, Lit. Matem. Sb., VI (1966), 321–346, (In Russian.) 0139.35302 Google Scholar[3] V. M. Zolotarev, An absolute estimate of the remainder term in the central limit theorem, Theory Prob. Applications, 11 (1966), 95–105, (English translation.) 10.1137/1111005 0154.43602 LinkGoogle Scholar[4] A. M. Lyapunov, Collected works. Vol. I, Izdat. Akad. Nauk SSSR, Moscow, 1954, 157–176, (In Russian.) MR0086006 Google Scholar[5] L. V. Osipov, Refinement of Lindeberg's theorem, Theory Prob. Applications, 9 (1966), 299–302, (English translation.) 10.1137/1111026 0147.37001 LinkGoogle Scholar[6] V. V. Petrov, A bound for the deviation of the distribution of a sum of independent random variables from the normal law, Dokl. Akad. Nauk SSSR, 160 (1965), 1013–1015, (In Russian.) MR0178497 Google Scholar[7] Andrew C. Berry, The accuracy of the Gaussian approximation to the sum of independent variates, Trans. Amer. Math. Soc., 49 (1941), 122–136 MR0003498 0025.34603 CrossrefGoogle Scholar[8] Carl-Gustav Esseen, Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law, Acta Math., 77 (1945), 1–125 MR0014626 0060.28705 CrossrefGoogle Scholar[9] Willy Feller, Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung, Math. Z., 40 (1936), 521–559 10.1007/BF01218878 MR1545580 0012.36102 CrossrefGoogle Scholar[10] Melvin L. Katz, Note on the Berry-Esseen theorem, Ann. Math. Statist., 34 (1963), 1107–1108 MR0151996 0122.36704 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Toward the History of the Saint Petersburg School of Probability and Statistics. I. 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