An estimator for the parameters of concentrations of two-component mixtures with censored data
Author:
A. Yu. Rizhov
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 76 (2008), 169-179
MSC (2000):
Primary 62N01; Secondary 62F12
DOI:
https://doi.org/10.1090/S0094-9000-08-00741-2
Published electronically:
July 17, 2008
MathSciNet review:
2368749
Full-text PDF Free Access
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Abstract: We consider a model of two-component mixtures with varying concentrations for the case of censored data. We find estimates for the concentrations of components and prove that the estimators are strongly consistent and asymptotically normal.
References
- E. L. Kaplan and Paul Meier, Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958), 457–481. MR 93867
- David W. Hosmer Jr. and Stanley Lemeshow, Applied survival analysis, Wiley Series in Probability and Statistics: Texts and References Section, John Wiley & Sons, Inc., New York, 1999. Regression modeling of time to event data; A Wiley-Interscience Publication. MR 1674644
- D. R. Cox and D. Oakes, Analysis of survival data, Monographs on Statistics and Applied Probability, Chapman & Hall, London, 1984. MR 751780
- 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
- R. E. Maĭboroda, Statistical Analysis of Mixtures, Kyiv University, Kyiv, 2003. (Ukrainian)
- Q. Yu and L. Li, On the strong uniform consistency of the product limit estimator, Sankhyā 56 (1994), 416–430.
- Patrick Billingsley, Convergence of probability measures, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0233396
References
- E. L. Kaplan and P. Meier, Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958), 457–481. MR 0093867 (20:387)
- D. W. Hosmer and S. Lemeshow, Applied Survival Analysis: Regression Modeling of Time to Event Data, J. Wiley & Sons, Inc., New York, 1999. MR 1674644 (2000c:62172)
- D. R. Cox and D. Oakes, Analysis of Survival Data, Chapman & Hall/CRC, London, 1984. MR 751780 (86f:62170)
- D. P. Harrington and T. R. Fleming, Counting Processes and Survival Analysis, J. Wiley & Sons, Inc., New York, 1991. MR 1100924 (92i:60091)
- R. E. Maĭboroda, Statistical Analysis of Mixtures, Kyiv University, Kyiv, 2003. (Ukrainian)
- Q. Yu and L. Li, On the strong uniform consistency of the product limit estimator, Sankhyā 56 (1994), 416–430.
- P. Billingsley, Convergence of Probability Measures, John Wiley & Sons, Inc., New York, 1968. MR 0233396 (38:1718)
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Additional Information
A. Yu. Rizhov
Affiliation:
Department of General Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
MR Author ID:
751027
ORCID:
0000-0003-4099-0742
Email:
ryzhov@univ.kiev.ua
Keywords:
Mixtures with varying concentrations,
censoring,
Kaplan–Meier estimator
Received by editor(s):
February 15, 2006
Published electronically:
July 17, 2008
Article copyright:
© Copyright 2008
American Mathematical Society
