Estimation of the smoothness of density

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.

Keywords:

• estimation
• histogram
• Besov spaces

AMS Subject Classification :

• 62G05
• 62G07
• 62G20
• 46B06
• 62G07
• 62G20

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