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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.
@article{PS_2014__18__130_0,
author = {Dziedziul, Karol and \'Cmiel, Bogdan},
title = {Density smoothness estimation problem using a wavelet approach},
journal = {ESAIM: Probability and Statistics},
pages = {130--144},
publisher = {EDP-Sciences},
volume = {18},
year = {2014},
doi = {10.1051/ps/2013030},
mrnumber = {3143736},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2013030/}
}
TY - JOUR AU - Dziedziul, Karol AU - Ćmiel, Bogdan TI - Density smoothness estimation problem using a wavelet approach JO - ESAIM: Probability and Statistics PY - 2014 SP - 130 EP - 144 VL - 18 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ps/2013030/ DO - 10.1051/ps/2013030 LA - en ID - PS_2014__18__130_0 ER -
%0 Journal Article %A Dziedziul, Karol %A Ćmiel, Bogdan %T Density smoothness estimation problem using a wavelet approach %J ESAIM: Probability and Statistics %D 2014 %P 130-144 %V 18 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ps/2013030/ %R 10.1051/ps/2013030 %G en %F PS_2014__18__130_0
Dziedziul, Karol; Ćmiel, Bogdan. Density smoothness estimation problem using a wavelet approach. ESAIM: Probability and Statistics, Tome 18 (2014), pp. 130-144. doi: 10.1051/ps/2013030
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