On the universal constant in the Katz-Petrov and Osipov inequalities

• Autorzy: Victor Korolev , Sergey Popov
• Języki publikacji: EN

Abstrakty

EN

Upper estimates are presented for the universal constant in the Katz-Petrov and Osipov inequalities which do not exceed 3.1905.

Słowa kluczowe

EN

central limit theorem; convergence rate estimate; absolute constant; Katz-Petrov inequality; Osipov inequality

Kategorie tematyczne

• 60G50: Sums of independent random variables; random walks
• 60F05: Central limit and other weak theorems

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2011
• Tom: 31
• Numer: 1-2
• Strony: 29-39

Daty

wydano

2011

otrzymano

2011-02-16

Twórcy

autor

Victor Korolev

• Faculty of Computational Mathematics and Cybernetics, Moscow State University, Institute for Informatics Problems, Russian Academy of Sciences

autor

Sergey Popov

• Faculty of Computational Mathematics and Cybernetics, Moscow State University

Bibliografia

• [1] R.N. Bhattacharya and R. Ranga Rao, Normal Approximation and Asymptotic Expansions (New York, Wiley, 1976).
• [2] L.H.Y. Chen and Q.M. Shao, A non-uniform Berry-Esseen bound via Stein's method, Probability Theory and Related Fields 120 (2001) 236-254.
• [3] W. Hoeffding, The extrema of the expected value of a function of independent random variables, Ann. Math. Statist. 19 (1948) 239-325.
• [4] M. Katz, Note on the Berry-Esseen theorem, Annals of Math. Statist. 39 (4) (1963) 1348-1349.
• [5] V.Yu. Korolev and I.G. Shevtsova, An improvement of the Berry-Esseen inequality with applications to Poisson and mixed Poisson random sums, Scandinavian Actuarial Journal, 2010. Online first: http://www.informaworld.com/10.1080/03461238.2010.485370, 04 June 2010.
• [6] J.S. Nefedova and I.G. Shevtsova, On non-uniform estimates of convergence rate in the central limit theorem, Theory Probab. Appl. 56 (2011), to appear.
• [7] L.V. Osipov, A refinement of the Lindeberg theorem, Theory Probab. Appl. 11 (2) (1966) 339-342.
• [8] L. Paditz, Bemerkungen zu einer Fehlerabschätzung im zentralen Grenzwertsatz, Wiss. Z. Hochschule für Verkehrswesen Friedrich List 27 (4) (1980) 829-837.
• [9] L. Paditz, On error-estimates in the central limit theorem for generalized linear discounting, Math. Operationsforsch. u. Statist., Ser. Statistics 15 (4) (1984) 601-610.
• [10] L. Paditz, Über eine Fehlerabschätzung im zentralen Grenzwertsatz, Wiss. Z. Hochschule für Verkehrswesen Friedrich List Dresden 33 (2) (1986) 399-404.
• [11] V.V. Petrov, An estimate of the deviation of the distribution of a sum of independent random variables from the normal law, Soviet Math. Dokl. 160 (5) (1965) 1013-1015.
• [12] V.V. Petrov, Sums of Independent Random Variables (New York, Springer, 1975).
• [13] I.G. Shevtsova, A refinement of the estimates of the rate of convergence in the Lyapunov theorem, Doklady Mathematics 435 (1) (2010) 26-28.

Identyfikatory

DOI

10.7151/dmps.1138