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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

An adaptive estimator of the density of components of a mixture


Author: D. I. Pokhyl'ko
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 74 (2006).
Journal: Theor. Probability and Math. Statist. 74 (2007), 147-162
MSC (2000): Primary 62G07; Secondary 42C40
Published electronically: July 5, 2007
MathSciNet review: 2336785
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Abstract | References | Similar Articles | Additional Information

Abstract: Linear and nonlinear wavelet estimators of the density of components of a mixture are considered in the paper. The rate of convergence in the uniform metric and large deviation probabilities are obtained for linear estimators. The limit behavior of the threshold-based estimator is considered for the integral metric. An adaptive modification of the threshold-based estimator is constructed.


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Additional Information

D. I. Pokhyl'ko
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Volodymyrs’ka Street, 64, Kyiv 01033, Ukraine
Email: pdi_2004@mail.ru

DOI: http://dx.doi.org/10.1090/S0094-9000-07-00704-1
PII: S 0094-9000(07)00704-1
Keywords: Wavelets, mixture, estimator of the density, adaptive estimator, projective estimator
Received by editor(s): June 27, 2005
Published electronically: July 5, 2007
Article copyright: © Copyright 2007 American Mathematical Society