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), 8392
MSC (2000):
Primary 62G05; Secondary 62G20
Published electronically:
August 5, 2005
Fulltext PDF Free Access
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
(97j:62055), http://dx.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
(2005g:62065)
 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
(2005i:62080), http://dx.doi.org/10.1090/S0094900005006174
 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
(2001g:60089)
 5.
A.
V. Skorokhod, Studies in the theory of random processes,
Translated from the Russian by Scripta Technica, Inc, AddisonWesley
Publishing Co., Inc., Reading, Mass., 1965. MR 0185620
(32 #3082b)
 6.
Patrick
Billingsley, Convergence of probability measures, John Wiley
& Sons, Inc., New YorkLondonSydney, 1968. MR 0233396
(38 #1718)
 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
(99k:62102)
 1.
 R. E. Maiboroda, Estimators of components of a mixture with varying concentrations, Ukrain. Mat. Zh. 48 (1996), no. 4, 562566; English transl. in Ukrainian Math. J. 48 (1997), no. 4, 618622. MR 1417019 (97j:62055)
 2.
 O. Kubachuk, Estimation of moments by observations from mixtures with varying concentrations, Theory Stoch. Process. 8(24) (2002), no. 34, 226232. MR 2027394 (2005g:62065)
 3.
 R. Maboroda and O. Kubachuk, Asymptotic normality of improved weighted empirical distribution functions, Teor. Imovirnost. ta Matem. Statist. 69 (2003), 8995; English transl. in Theor. Probability and Math. Statist. 69 (2004), 95102. MR 2110908
 4.
 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)
 5.
 A. V. Skorokhod, Studies in the Theory of Random Processes, Kiev University, Kiev, 1961; English transl., AddisonWesley Publishing Co., Inc., Reading, Mass., 1965. MR 0185620 (32:3082b)
 6.
 P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968. MR 0233396 (38:1718)
 7.
 R. E. Maboroda, Correlation analysis of mixtures. I, Teor. Imovirnost. ta Matem. Statist. 54 (1996), 105115; English transl. in Theor. Probability and Math. Statist. 54 (1997), 105114. MR 1644590 (99k:62102)
Similar Articles
Retrieve articles in Theory of Probability and Mathematical Statistics
with MSC (2000):
62G05,
62G20
Retrieve articles in all journals
with MSC (2000):
62G05,
62G20
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:
http://dx.doi.org/10.1090/S0094900005006423
PII:
S 00949000(05)006423
Received by editor(s):
January 22, 2003
Published electronically:
August 5, 2005
Article copyright:
© Copyright 2005
American Mathematical Society
