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Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

 
 

 

The convergence of $U$-statistics and von Mises functionals in the mean metric


Author: Sh. Sharakhmetov
Translated by: Oleg Klesov
Journal: Theor. Probability and Math. Statist. 68 (2004), 167-172
MSC (2000): Primary 60F05
DOI: https://doi.org/10.1090/S0094-9000-04-00589-7
Published electronically: May 11, 2004
MathSciNet review: 2000646
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove global limit theorems for $U$-statistics and von Mises functionals. The rate of convergence in these theorems is also obtained.


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References
  • L. J. Serfling, Approximation theorems of mathematical statistics, Wiley, New York, 1980. MR 82a:62003
  • V. S. Korolyuk and Yu. V. Borovskikh, Theory of $U$ statistics, “Naukova dumka", Kiev, 1989; English transl., Kluwer, Dordrecht, 1993. MR 90k:60044
  • P. K. Sen, Sequential nonparametrics: invariance principles and statistical inference, Wiley, New York, 1981. MR 83c:62128
  • V. M. Zolotarev, A modern theory of summation of independent random variables, “Nauka", Moscow, 1986. (Russian) MR 89a:60003
  • Sh. Sharakhmetov, Global limit theorems for $U$-statistic and von Mises functional, Proceed. 5th Vilnius Conf., Vilnius, 1989. (Russian)
  • V. M. Kruglov, Global limit theorems, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) VIII (1976), 84–101. MR 55:4324
  • V. V. Petrov, Limit theorems for sums of independent random variables, “Nauka", Moscow, 1987; English transl., Oxford Univ. Press, Oxford, 1991. MR 88i:60004
  • R. Michel, On the constant in the nonuniform version of the Berry–Esseen theorem, Z. Wahrscheinlichkeitstheorie verw. Gebiete 55 (1981), 109–117. MR 82c:60042
  • C. Gini, Di una misura delle relazioni tra le graduatorie di due caratteri, Ludovico Cecehini, Rome, 1914.

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Additional Information

Sh. Sharakhmetov
Affiliation: Tashkent University for Economics, Uzbekistanskii prospekt 49, Tashkent 700063, Uzbekistan

Received by editor(s): September 1, 1999
Published electronically: May 11, 2004
Article copyright: © Copyright 2004 American Mathematical Society