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A test of the hypothesis about the homogeneity of components of a mixture with varying concentrations by using censored data
Author(s):
A.
Yu.
Ryzhov
Translated by:
S. Kvasko
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 72
(2005).
Journal:
Theor. Probability and Math. Statist.
No. 72
(2006),
145-155.
MSC (2000):
Primary 62N03;
Secondary 62G10
Posted:
September 5, 2006
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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:
-
- 1.
- D. R. Cox and D. Oakes, Analysis of Survival Data, Chapman & Hall, New York, 1984. MR 0751780 (86f:62170)
- 2.
- R. E. Ma
boroda, Statistical Analysis of Mixtures, Kyiv University, Kyiv, 2003. (Ukrainian) - 3.
- E. L. Kaplan and P. Meier, Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958), 457-481. MR 0093867 (20:387)
- 4.
- 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)
- 5.
- P. Billingsley, Convergence of Probability Measures, J. Wiley & Sons, Inc., New York, 1999. MR 1700749 (2000e:60008)
- 6.
- D. P. Harrington and T. R. Fleming, Counting Processes and Survival Analysis, J. Wiley & Sons, Inc., New York, 1991. MR 1100924 (92i:60091)
- 7.
- 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
Email:
ryzhov@univ.kiev.ua
DOI:
10.1090/S0094-9000-06-00672-7
PII:
S 0094-9000(06)00672-7
Keywords:
Survival analysis,
mixtures with varying concentrations,
censoring,
Kaplan--Meier estimator,
dispersion coefficient.
Received by editor(s):
5/JUL/2004
Posted:
September 5, 2006
Copyright of article:
Copyright
2006,
American Mathematical Society
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