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
Journal:
Theor. Probability and Math. Statist. 78 (2009), 133-146
MSC (2000):
Primary 60B12
DOI:
https://doi.org/10.1090/S0094-9000-09-00767-4
Published electronically:
August 4, 2009
MathSciNet review:
2446854
Full-text PDF Free Access
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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
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References
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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
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
