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

 

Estimates of distributions of components in a mixture from censoring data


Author: A. Yu. Ryzhov
Translated by: V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 69 (2003).
Journal: Theor. Probability and Math. Statist. 69 (2004), 167-174
MSC (2000): Primary 62N02; Secondary 62G05
Published electronically: February 9, 2005
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Abstract | References | Similar Articles | Additional Information

Abstract: The problem of estimation of the distribution functions of components in a mixture in the case of censored observations is considered. Optimal estimators are found in the class of linear estimators. Since the optimal estimators depend on unknown distribution functions of components, an adaptive estimation scheme is used. The asymptotic normality is proved for adaptive estimators and it is shown that their concentration coefficient coincides with that of the optimal linear estimator.


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Additional Information

A. Yu. Ryzhov
Affiliation: Department of Mathematics, Faculty of Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: tosha@ucr.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-05-00623-X
PII: S 0094-9000(05)00623-X
Keywords: Survival analysis, mixtures with varying concentrations, censoring, Kaplan--Meier estimators, concentration coefficient
Received by editor(s): February 14, 2003
Published electronically: February 9, 2005
Article copyright: © Copyright 2005 American Mathematical Society