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
Full-text PDF Free Access
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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.
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.
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