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Theory of Probability and Mathematical Statistics

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Asymptotic normality of improved weighted empirical distribution functions


Authors: R. Maiboroda and O. Kubaichuk
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 69 (2003).
Journal: Theor. Probability and Math. Statist. 69 (2004), 95-102
MSC (2000): Primary 62G30; Secondary 62G20
DOI: https://doi.org/10.1090/S0094-9000-05-00617-4
Published electronically: February 8, 2005
MathSciNet review: 2110908
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Abstract | References | Similar Articles | Additional Information

Abstract: Weighted empirical distribution functions are often used to estimate the distributions of components in a mixture. However, weighted empirical distribution functions do not possess some properties of probability distribution functions in the case of negative weight coefficients. We consider a method allowing one to improve weighted empirical distribution functions and obtain an estimator that is a distribution function. We prove that this estimator is asymptotically normal. The limit distribution of the improved weighted empirical distribution function coincides with that of the initial estimator.


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

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Additional Information

R. Maiboroda
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty of Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: mre@mechmat.univ.kiev.ua

O. Kubaichuk
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty of Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: linsta@akcecc.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-05-00617-4
Received by editor(s): September 26, 2002
Published electronically: February 8, 2005
Article copyright: © Copyright 2005 American Mathematical Society

American Mathematical Society