Density smoothness estimation problem using a wavelet approach
ESAIM: Probability and Statistics, Tome 18 (2014) , pp. 130-144.

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.

DOI : https://doi.org/10.1051/ps/2013030
Classification : 62G05,  62G07
Mots clés : estimation, wavelets, Besov spaces, smoothness parameter
@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://www.numdam.org/articles/10.1051/ps/2013030/}
}
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. http://www.numdam.org/articles/10.1051/ps/2013030/

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