Theory of Probability and Mathematical Statistics

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ISSN 1547-7363(e) ISSN 0094-9000(p)

Asymptotic normality of improved weighted empirical distribution functions

Author(s): R. Maiboroda; O. Kubaichuk
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 69 (2003).
Journal: Theor. Probability and Math. Statist. No. 69 (2004), 95-102.
MSC (2000): Primary 62G30; Secondary 62G20
Posted: 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:

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