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On Some Limit Theorems Involving the Empirical Distribution Function

Published online by Cambridge University Press:  20 November 2018

Miklós Csörgo
Miklós Csörgo*
Affiliation:
McGill University
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Let X1 …, Xn be mutually independent random variables with a common continuous distribution function F (t). Let Fn(t) be the corresponding empirical distribution function, that is

Fn(t) = (number of Xi ≤ t, 1 ≤ i ≤ n)/n.

Using a theorem of Manija [4], we proved among others the following statement in [1].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 5 , December 1967 , pp. 739 - 741
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Csörgo, M.(1966). Exact and limiting probability distributions of some Smirmovtype statistics. Canad. Math. Bull. 8, pp. 93-103.Google Scholar
2. Donsker, M. D. (1955). Justification and extension of Doob's heuristic approach to the Kolmogorov-Smirnov Theorems. Ann. Math. Statist. 23, pp. 277-281.Google Scholar
3. Doob, J. L. (1944). Heuristic approach to the Kolmogorov- Smirnov theorems. Ann. Math. Statist. 20, pp. 393-403.Google Scholar
4. Manija, G. M., (1944). Obobschenije Kriterija A. N. Kolmogorova dlja otcenkizakona racpredelenija po empirichesk imdannym. Dokl. Akad. Nauk. SSSR 69, pp. 495-497.Google Scholar
5. Quade, Dana (1966). On the asymptotic power of the one-sample Kolmogorov-Smirnov tests. Ann. Math. Statist. 36, pp. 1000-1018.Google Scholar