| Issue |
ESAIM: PS
Volume 18, 2014
|
|
|---|---|---|
| Page(s) | 130 - 144 | |
| DOI | https://doi.org/10.1051/ps/2013030 | |
| Published online | 28 November 2013 | |
Density smoothness estimation problem using a wavelet approach
1
Faculty of Applied Mathematics, Gdańsk University of Technology,
ul. G. Narutowicza
11/12, 80-233
Gdańsk,
Poland
kdz@mifgate.pg.gda.pl
2
Faculty of Applied Mathematics, AGH University of Science and
Technology, Al. Mickiewicza
30, 30-059
Cracov,
Poland
cmielbog@gmail.com
Received: 17 July 2012
Revised: 29 October 2012
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.
Mathematics Subject Classification: 62G05 / 62G07
Key words: Estimation / wavelets / Besov spaces / smoothness parameter
© EDP Sciences, SMAI, 2013
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