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The convergence of  -statistics and von Mises functionals in the mean metric
Author(s):
Sh.
Sharakhmetov
Translated by:
Oleg Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 68
(2003).
Journal:
Theor. Probability and Math. Statist.
No. 68
(2004),
167-172.
MSC (2000):
Primary 60F05
Posted:
May 11, 2004
MathSciNet review:
2000646
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Abstract:
We prove global limit theorems for  -statistics and von Mises functionals. The rate of convergence in these theorems is also obtained.
References:
-
- 1.
- L. J. Serfling, Approximation theorems of mathematical statistics, Wiley, New York, 1980. MR 82a:62003
- 2.
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 statistics, ``Naukova dumka", Kiev, 1989; English transl., Kluwer, Dordrecht, 1993. MR 90k:60044 - 3.
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- 4.
- V. M. Zolotarev, A modern theory of summation of independent random variables, ``Nauka", Moscow, 1986. (Russian) MR 89a:60003
- 5.
- Sh. Sharakhmetov, Global limit theorems for
 -statistic and von Mises functional, Proceed. 5th Vilnius Conf., Vilnius, 1989. (Russian) - 6.
- V. M. Kruglov, Global limit theorems, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) VIII (1976), 84-101. MR 55:4324
- 7.
- V. V. Petrov, Limit theorems for sums of independent random variables, ``Nauka", Moscow, 1987; English transl., Oxford Univ. Press, Oxford, 1991. MR 88i:60004
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- 9.
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Additional Information:
Sh.
Sharakhmetov
Affiliation:
Tashkent University for Economics, Uzbekistanskii prospekt 49, Tashkent 700063, Uzbekistan
DOI:
10.1090/S0094-9000-04-00589-7
PII:
S 0094-9000(04)00589-7
Received by editor(s):
1/SEP/1999
Posted:
May 11, 2004
Copyright of article:
Copyright
2004,
American Mathematical Society
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