Improved estimators for moments constructed from observations of a mixture
Authors:
R. Maĭboroda and O. Kubaĭchuk
Translated by:
V. Semenov
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
MathSciNet review:
2109826
Full-text PDF Free Access
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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.
References
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References
- R. E. Maĭboroda, Estimators of components of a mixture with varying concentrations, Ukrain. Mat. Zh. 48 (1996), no. 4, 562–566; English transl. in Ukrainian Math. J. 48 (1997), no. 4, 618–622. MR 1417019 (97j:62055)
- O. Kubaĭchuk, Estimation of moments by observations from mixtures with varying concentrations, Theory Stoch. Process. 8(24) (2002), no. 3–4, 226–232. MR 2027394 (2005g:62065)
- R. Maĭboroda and O. Kubaĭchuk, Asymptotic normality of improved weighted empirical distribution functions, Teor. Imovirnost. ta Matem. Statist. 69 (2003), 89–95; English transl. in Theor. Probability and Math. Statist. 69 (2004), 95–102. MR 2110908
- V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, TViMS, Kiev, 1998; English transl., American Mathematical Society, Providence, RI, 2000. MR 1743716 (2001g:60089)
- A. V. Skorokhod, Studies in the Theory of Random Processes, Kiev University, Kiev, 1961; English transl., Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965. MR 0185620 (32:3082b)
- P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968. MR 0233396 (38:1718)
- R. E. Maĭboroda, Correlation analysis of mixtures. I, Teor. Imovirnost. ta Matem. Statist. 54 (1996), 105–115; English transl. in Theor. Probability and Math. Statist. 54 (1997), 105–114. MR 1644590 (99k:62102)
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Additional Information
R. Maĭboroda
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. Kubaĭchuk
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
Received by editor(s):
January 22, 2003
Published electronically:
August 5, 2005
Article copyright:
© Copyright 2005
American Mathematical Society
