Estimation of the density of a distribution from data with an admixture
Authors:
N. Lodatko and R. Maiboroda
Translated by:
S. Kvasko
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 73 (2005).
Journal:
Theor. Probability and Math. Statist. 73 (2006), 99108
MSC (2000):
Primary 62G07; Secondary 62G20
Published electronically:
January 17, 2007
MathSciNet review:
2213844
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: We consider the problem of estimation of a density from observations of a twocomponent mixture with varying concentrations. It is assumed that the distribution of the first component is unknown, while a parametric model is (perhaps) available for the second component. Applying the sieve maximum likelihood method we construct histogramtype estimators for the densities of distributions of the components and estimators for unknown parameters of the second component. We prove the consistency of the estimators and obtain estimates for the rate of convergence.
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Additional Information
N. Lodatko
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
lodatko@yandex.ru
R. Maiboroda
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
mre@univ.kiev.ua
DOI:
http://dx.doi.org/10.1090/S0094900007006849
PII:
S 00949000(07)006849
Keywords:
Sieve maximum likelihood method,
histogram,
a mixture with varying concentrations,
consistency
Received by editor(s):
December 4, 2004
Published electronically:
January 17, 2007
Article copyright:
© Copyright 2007
American Mathematical Society
