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

 

Wavelet estimators of a density constructed from observations of a mixture


Author: D. Pokhyl'ko
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 70 (2004).
Journal: Theor. Probability and Math. Statist. 70 (2005), 135-145
MSC (2000): Primary 62G07; Secondary 42C40
Published electronically: August 12, 2005
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Abstract | References | Similar Articles | Additional Information

Abstract: We construct projective estimators of a density by using a wavelet basis for the data being a sample from a mixture of several components whose concentrations vary with observations. We construct linear and adaptive estimators and prove that they converge in the mean square norm. We also prove that the linear estimator converges in the uniform norm.


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Additional Information

D. Pokhyl'ko
Affiliation: Department of Probability Theory and Mathematical Statistics, Mechanics and Mathematics Faculty, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: pokhid@ukr.net

DOI: http://dx.doi.org/10.1090/S0094-9000-05-00637-X
PII: S 0094-9000(05)00637-X
Keywords: Wavelets, projective estimators of a density, estimation of components in a mixture
Received by editor(s): March 14, 2003
Published electronically: August 12, 2005
Article copyright: © Copyright 2005 American Mathematical Society