Improved estimators for moments constructed from observations of a mixture

Authors:
R. Maiboroda and O. Kubaichuk

Translated by:
V. Semenov

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **70** (2004).

Journal:
Theor. Probability and Math. Statist. **70** (2005), 83-92

MSC (2000):
Primary 62G05; Secondary 62G20

DOI:
https://doi.org/10.1090/S0094-9000-05-00642-3

Published electronically:
August 5, 2005

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Procedures for improving weighted empirical distribution functions constructed from mixtures with varying concentrations are considered. The procedures are such that the estimators of moments of the mixture components constructed from weighted empirical distribution functions have specified properties (say, estimators of the variance must not be negative). We prove that the moment estimators constructed from improved weighted empirical distribution functions have the same asymptotic behavior as those constructed from the original weighted empirical distribution functions.

**1.**R. Ē. Maĭboroda,*Estimation of the distributions of the components of mixtures having varying concentrations*, Ukraïn. Mat. Zh.**48**(1996), no. 4, 558–562 (Ukrainian, with English and Ukrainian summaries); English transl., Ukrainian Math. J.**48**(1996), no. 4, 618–622 (1997). MR**1417019**, https://doi.org/10.1007/BF02390622**2.**O. Kubaychuk,*Estimation of moments by observations from mixtures with varying concentrations*, Proceedings of the Conference Dedicated to the 90th Anniversary of Boris Vladimirovich Gnedenko (Kyiv, 2002), 2002, pp. 226–231. MR**2027394****3.**R. Maĭboroda and O. Kubaĭchuk,*Asymptotic normality of improved weighted empirical distribution functions*, Teor. Ĭmovīr. Mat. Stat.**69**(2003), 89–95 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist.**69**(2004), 95–102 (2005). MR**2110908**, https://doi.org/10.1090/S0094-9000-05-00617-4**4.**V. V. Buldygin and Yu. V. Kozachenko,*Metric characterization of random variables and random processes*, Translations of Mathematical Monographs, vol. 188, American Mathematical Society, Providence, RI, 2000. Translated from the 1998 Russian original by V. Zaiats. MR**1743716****5.**A. V. Skorokhod,*Studies in the theory of random processes*, Translated from the Russian by Scripta Technica, Inc, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965. MR**0185620****6.**Patrick Billingsley,*Convergence of probability measures*, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR**0233396****7.**R. Ē. Maĭboroda,*Correlation analysis of mixtures. I*, Teor. Ĭmovīr. Mat. Stat.**54**(1996), 99–108 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist.**54**(1997), 105–114. MR**1644590**

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Additional Information

**R. Maiboroda**

Affiliation:
Department of Probability Theory and Mathematical Statistics, Mechanics and Mathematics Faculty, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine

Email:
mre@mechmat.univ.kiev.ua

**O. Kubaichuk**

Affiliation:
Department of Probability Theory and Mathematical Statistics, Mechanics and Mathematics Faculty, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine

Email:
linsta@akcecc.kiev.ua

DOI:
https://doi.org/10.1090/S0094-9000-05-00642-3

Received by editor(s):
January 22, 2003

Published electronically:
August 5, 2005

Article copyright:
© Copyright 2005
American Mathematical Society