Estimates of distributions of components in a mixture from censoring data
Author:
A. Yu. Ryzhov
Translated by:
V. Semenov
Journal:
Theor. Probability and Math. Statist. 69 (2004), 167-174
MSC (2000):
Primary 62N02; Secondary 62G05
DOI:
https://doi.org/10.1090/S0094-9000-05-00623-X
Published electronically:
February 9, 2005
MathSciNet review:
2110914
Full-text PDF Free Access
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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
- D. R. Cox and D. Oakes, Analysis of survival data, Monographs on Statistics and Applied Probability, Chapman & Hall, London, 1984. MR 751780
- E. L. Kaplan and Paul Meier, Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958), 457–481. MR 93867
- Thomas R. Fleming and David P. Harrington, Counting processes and survival analysis, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, John Wiley & Sons, Inc., New York, 1991. MR 1100924
References
- D. R. Cox and D. Oakes, Analysis of Survival Data, Chapman & Hall, New York, 1984. MR 0751780 (86f:62170)
- E. L. Kaplan and P. Meier, Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958), 457–481. MR 0093867 (20:387)
- 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
MR Author ID:
751027
ORCID:
0000-0003-4099-0742
Email:
tosha@ucr.kiev.ua
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
