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

Full-text PDF Free Access

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.

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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