A test of the hypothesis about the homogeneity of components of a mixture with varying concentrations by using censored data
Author:
A. Yu. Ryzhov
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 72 (2006), 145-155
MSC (2000):
Primary 62N03; Secondary 62G10
DOI:
https://doi.org/10.1090/S0094-9000-06-00672-7
Published electronically:
September 5, 2006
MathSciNet review:
2168144
Full-text PDF Free Access
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Additional Information
Abstract: We consider a statistical test for the homogeneity of components in a model of mixtures with varying concentrations by using censored data. The test is constructed with the help of adaptive estimators of components of a mixture.
References
- D. R. Cox and D. Oakes, Analysis of survival data, Monographs on Statistics and Applied Probability, Chapman & Hall, London, 1984. MR 751780
- R. E. Maĭboroda, Statistical Analysis of Mixtures, Kyiv University, Kyiv, 2003. (Ukrainian)
- E. L. Kaplan and Paul Meier, Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958), 457–481. MR 93867
- A. Yu. Rizhov, Estimates for the distributions of components of a mixture based on censored data, Teor. Ĭmovīr. Mat. Stat. 69 (2003), 154–161 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 69 (2004), 167–174 (2005). MR 2110914, DOI https://doi.org/10.1090/S0094-9000-05-00623-X
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- A. Ya. Dorogovtsev, D. S. Silvestrov, A. V. Skorokhod, and M. I. Yadrenko, Probability theory: collection of problems, Translations of Mathematical Monographs, vol. 163, American Mathematical Society, Providence, RI, 1997. Translated from the 1976 Ukrainian original by O. I. Klesov and V. A. Kotov. MR 1444579
References
- D. R. Cox and D. Oakes, Analysis of Survival Data, Chapman & Hall, New York, 1984. MR 0751780 (86f:62170)
- R. E. Maĭboroda, Statistical Analysis of Mixtures, Kyiv University, Kyiv, 2003. (Ukrainian)
- E. L. Kaplan and P. Meier, Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958), 457–481. MR 0093867 (20:387)
- A. Yu. Ryzhov, Estimates of distributions of components in a mixture from censoring data, Teor. Imovir. ta Matem. Statist. 69 (2003), 140–147; English transl. in Theory Probab. Math. Statist. 69 (2004), 167–174. MR 2110914 (2005i:62138)
- P. Billingsley, Convergence of Probability Measures, J. Wiley & Sons, Inc., New York, 1999. MR 1700749 (2000e:60008)
- D. P. Harrington and T. R. Fleming, Counting Processes and Survival Analysis, J. Wiley & Sons, Inc., New York, 1991. MR 1100924 (92i:60091)
- A. Ya. Dorogovtsev, D. S. Silvestrov, A. V. Skorokhod, and M. I Yadrenko, Probability Theory: Collection of Problems, “Vyshcha Shkola”, Kyiv, 1976; English transl., American Mathematical Society, Providence, RI, 1997. MR 1444579 (98k:60001)
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Additional Information
A. Yu. Ryzhov
Affiliation:
Department of General Mathematics, Faculty for Mathematics and Mechanics, 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:
Survival analysis,
mixtures with varying concentrations,
censoring,
Kaplan–Meier estimator,
dispersion coefficient.
Received by editor(s):
July 5, 2004
Published electronically:
September 5, 2006
Article copyright:
© Copyright 2006
American Mathematical Society
