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Wavelet estimators of a density constructed from observations of a mixture
Author(s):
D.
Pokhyl'ko
Translated by:
Oleg Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 70
(2004).
Journal:
Theor. Probability and Math. Statist.
No. 70
(2005),
135-145.
MSC (2000):
Primary 62G07;
Secondary 42C40
Posted:
August 12, 2005
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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.
References:
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- 2.
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- Ingrid Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1996. MR 1162107 (93e:42045)
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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:
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):
14/MAR/2003
Posted:
August 12, 2005
Copyright of article:
Copyright
2005,
American Mathematical Society
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