Abstract
This paper introduces a definition where the smoothness of a function f is characterized by means of the Besov spaces , that is, there is the parameter s* such that for all s<s*, , and for all s>s*, . If f is a density with the smoothness s*, then we construct an estimator of s* which is based on histograms.
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Acknowledgements
The author is supported in part by the grant ‘The exploitation of white cabbage for phytoremediation and biofumigation of soils (AGROBIOKAP)’ co-financed by the European Union from European Regional Development Fund in a framework of the Innovative Economy Operational Programme 2007–2013