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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Improved estimators for moments constructed from observations of a mixture


Authors: R. Maiboroda and O. Kubaichuk
Translated by: V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 70 (2004).
Journal: Theor. Probability and Math. Statist. 70 (2005), 83-92
MSC (2000): Primary 62G05; Secondary 62G20
Published electronically: August 5, 2005
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Abstract | References | Similar Articles | Additional Information

Abstract: Procedures for improving weighted empirical distribution functions constructed from mixtures with varying concentrations are considered. The procedures are such that the estimators of moments of the mixture components constructed from weighted empirical distribution functions have specified properties (say, estimators of the variance must not be negative). We prove that the moment estimators constructed from improved weighted empirical distribution functions have the same asymptotic behavior as those constructed from the original weighted empirical distribution functions.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0094-9000-05-00642-3
PII: S 0094-9000(05)00642-3
Received by editor(s): January 22, 2003
Published electronically: August 5, 2005
Article copyright: © Copyright 2005 American Mathematical Society