A Journal "Theory of Probability and Mathematical Statistics"
2024
2023
2022
2021
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
1972
1971
1970


Archive

About   Editorial Board   Contacts   Template   Publication Ethics   Peer Review Process   Special Issues   History  

Theory of Probability and Mathematical Statistics



A modified Kaplan-Meier estimator for a model of mixtures with varying concentrations

R. E. Maĭboroda, V. G. Khizanov

Download PDF

Abstract: A modified Kaplan-Meier estimator for the distribution of components of a mixture with varying concentrations is constructed from censored data. The consistency of the estimators in the uniform norm is proved and the upper bound for the rate of convergence is derived.

Keywords: Kaplan-Meier estimator, models of mixtures with varying concentrations, consistency, censoring

Bibliography:
1. O. Korosteleva, Clinical Statistics: Introducing Clinical Trials, Survival Analysis, and Longitudinal Data Analysis, Jones and Bartlett Publishers, Sudbury, MA, 2008.
2. C. Huber, N. Limnios, M. Mesbah, and M. Nikulin, Mathematical Methods in Survival Analysis, Reliability and Quality of Life, ISTE/Wiley, London/Hoboken, NJ, 2008.
3. J. Shao, Mathematical Statistics, Springer-Verlag, New York, 1998.
4. R. Maĭboroda and O. Sugakova, Statistics of mixtures with varying concentrations with application to DNA microarray data analysis, J. Nonparametric Statist. 24 (2012), no. 1, 201-215.
5. R. E. Maĭboroda and O. V. Sugakova, Estimation and classification by using observations sampled from a mixture, Kyiv University'', Kyiv, 2008. (Ukrainian)
6. A. Yu. Ryzhov, Estimates of distributions of components in a mixture from censoring data, Teor. Ĭmovir. Mat. Stat. 69 (2003), 154-161; English transl. in Theor. Probability and Math. Statist. 69 (2004), 167-174.
7. A. Shcherbina, Estimation of the mean value in a model of mixtures with varying concentrations, Teor. Ĭmovir. Mat. Stat. 84 (2011), 142-154; English transl. in Theor. Probability and Math. Statist. 84 (2012), 151-164.
8. F. Autin and C. Pouet, Minimax rates over Besov spaces in ill-conditioned mixture-models with varying mixing-weights, J. Statist. Plann. Inference 146 (2014), 20-30.
9. R. D. Gill and S. Johansen, A Survey of product-integration with a view toward application in survival analysis, Ann. Statist. 18 (1990), no. 4, 1501-1555.