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

Full-text PDF Free Access

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

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