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THE SEQUENTIAL UNIFORM LAW OF LARGE NUMBERS
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 Title & Authors
THE SEQUENTIAL UNIFORM LAW OF LARGE NUMBERS
Bae, Jong-Sig; Kim, Sung-Yeun;
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 Abstract
Let be the sequential empirical process based on the independent and identically distributed random variables. We prove that convergence problems of to zero boil down to those of . We employ Ottaviani's inequality and the complete convergence to establish, under bracketing entropy with the second moment, the almost sure convergence of to zero.
 Keywords
sequential Glivenko-Cantelli class;Ottaviani's inequality;complete convergence;almost sure convergence;uniform law of large numbers;
 Language
English
 Cited by
 References
1.
P. Billingsley, Convergence of probability measure, John Wiely & Sons, New York, 1968

2.
J. DeHardt, Generalizations of the Glivenko-Cantelli theorem, Ann. Math. Statist. 42 (1971), 2050-2055 crossref(new window)

3.
P. Erdos, On a theorem of Hsu and Robbins, Ann. Math. Statist. 20 (1949), 286-291 crossref(new window)

4.
P. L. Hsu and H. Robbins, Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci. U. S. A. 33 (1947), 25-31

5.
A. F. Karr, Probability, Springer Texts in Statistics, Springer-Verlag, New York, 1993

6.
S. Shreve, Stochastic calculus and finance, Springer Finance, Springer-Verlag, New York, 2004

7.
S. van de Geer, Empirical processes in M-estimation, Cambridge in Statististical and Probabilistic Mathematics (Cambridge University Press, Cambridge, United Kingdom, 2000

8.
A. W. van der Vaart and J. A. Wellner, Weak convergence and empirical processes with applications to statistics, Springer series in Statistics, Springer-Verlag, New York, 1996