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An estimator for the parameters of concentrations of two-component mixtures with censored data
Author(s):
A.
Yu.
Rizhov
Translated by:
N. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 76
(2007).
Journal:
Theor. Probability and Math. Statist.
No. 76
(2008),
169-179.
MSC (2000):
Primary 62N01;
Secondary 62F12
Posted:
July 17, 2008
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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:
-
- 1.
- E. L. Kaplan and P. Meier, Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958), 457-481. MR 0093867 (20:387)
- 2.
- 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)
- 3.
- D. R. Cox and D. Oakes, Analysis of Survival Data, Chapman & Hall/CRC, London, 1984. MR 751780 (86f:62170)
- 4.
- D. P. Harrington and T. R. Fleming, Counting Processes and Survival Analysis, J. Wiley & Sons, Inc., New York, 1991. MR 1100924 (92i:60091)
- 5.
- R. E. Maĭboroda, Statistical Analysis of Mixtures, Kyiv University, Kyiv, 2003. (Ukrainian)
- 6.
- Q. Yu and L. Li, On the strong uniform consistency of the product limit estimator, Sankhyā 56 (1994), 416-430.
- 7.
- 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
Email:
ryzhov@univ.kiev.ua
DOI:
10.1090/S0094-9000-08-00741-2
PII:
S 0094-9000(08)00741-2
Keywords:
Mixtures with varying concentrations,
censoring,
Kaplan--Meier estimator
Received by editor(s):
15/FEB/2006
Posted:
July 17, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
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