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Density smoothness estimation problem usinga wavelet approach

Published online by Cambridge University Press:  28 November 2013

Karol Dziedziul  and
Bogdan Ćmiel
Karol Dziedziul
Affiliation:
Faculty of Applied Mathematics, Gdańsk University of Technology, ul. G. Narutowicza 11/12, 80-233 Gdańsk, Poland. kdz@mifgate.pg.gda.pl
Bogdan Ćmiel
Affiliation:
Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Cracov, Poland; cmielbog@gmail.com
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Abstract

In this paper we consider a smoothness parameter estimation problem for a density function. The smoothness parameter of a function is defined in terms of Besov spaces. This paper is an extension of recent results (K. Dziedziul, M. Kucharska, B. Wolnik, Estimation of the smoothness parameter). The construction of the estimator is based on wavelets coefficients. Although we believe that the effective estimation of the smoothness parameter is impossible in general case, we can show that it becomes possible for some classes of the density functions.

Keywords

EstimationwaveletsBesov spacessmoothness parameter
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 18 , 2014 , pp. 130 - 144
Copyright
© EDP Sciences, SMAI, 2013

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