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Title: Asymptotic normality of improved weighted empirical distribution functions
Authors: Кубайчук, Оксани Олексіївни
Майборода, Р.Є
Keywords: Weighted empirical distribution functions
Issue Date: 2004
Publisher: Theory Probab. Math. Stat
Citation: 2. Kubaychuk O.. Asymptotic normality of improved weighted empirical distribution functions/ Majboroda R // Theory Probab. Math. Stat. – 2004. № 69, Р.95–102.
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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