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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Some applications of the Gnedenko-Korolyuk method to empirical distributions


Authors: E. O. Lutsenko, O. V. Marinich and I. K. Matsak
Translated by: O. I. Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 78 (2008).
Journal: Theor. Probability and Math. Statist. 78 (2009), 133-146
MSC (2000): Primary 60B12
Published electronically: August 4, 2009
MathSciNet review: 2446854
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Abstract | References | Similar Articles | Additional Information

Abstract: A new proof of the Kolmogorov theorem on the asymptotic behavior of the deviation between a theoretical and an empirical distribution function is presented. We use the Gnedenko-Korolyuk approach based on some combinatorial properties of the merged sample constructed from two other independent samples. Some statistical applications of the Gnedenko-Korolyuk theorem are discussed.


References [Enhancements On Off] (What's this?)

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Additional Information

E. O. Lutsenko
Affiliation: Department of Operation Research, Faculty for Cybernetics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: ievgen_lutsenko@ukr.net

O. V. Marinich
Affiliation: Department of Operation Research, Faculty for Cybernetics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: marinich@voliacable.com

I. K. Matsak
Affiliation: Department of Operation Research, Faculty for Cybernetics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: mik@unicyb.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-09-00767-4
PII: S 0094-9000(09)00767-4
Keywords: Empirical distribution function, Kolmogorov theorem, Gnedenko--Korolyuk method
Received by editor(s): July 2, 2007
Published electronically: August 4, 2009
Article copyright: © Copyright 2009 American Mathematical Society