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Estimates of distributions of components in a mixture from censoring data

Author(s): A. Yu. Ryzhov
Translated by: V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 69 (2003).
Journal: Theor. Probability and Math. Statist. No. 69 (2004), 167-174.
MSC (2000): Primary 62N02; Secondary 62G05
Posted: February 9, 2005
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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.

References:

1.: D. R. Cox and D. Oakes, Analysis of Survival Data, Chapman & Hall, New York, 1984. MR 0751780 (86f:62170)
2.: E. L. Kaplan and P. Meier, Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958), 457-481. MR 0093867 (20:387)
3.: D. P. Harrington and T. R. Fleming, Counting Processes and Survival Analysis, Wiley, New York, 1991. MR 1100924 (92i:60091)

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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: 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): 14/FEB/2003
Posted: February 9, 2005
Copyright of article: Copyright 2005, American Mathematical Society


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