Estimation of a smoothness parameter by spline wavelets

• Autorzy: Magdalena Meller , Natalia Jarzębkowska
• Języki publikacji: EN

Abstrakty

EN

We consider the smoothness parameter of a function f ∈ L²(ℝ) in terms of Besov spaces $B^{s}_{2,∞}(ℝ)$,
$s*(f) = sup{s > 0: f ∈ B^{s}_{2,∞}(ℝ)}$.
The existing results on estimation of smoothness [K. Dziedziul, M. Kucharska and B. Wolnik, J. Nonparametric Statist. 23 (2011)] employ the Haar basis and are limited to the case 0 < s*(f) < 1/2. Using p-regular (p ≥ 1) spline wavelets with exponential decay we extend them to density functions with 0 < s*(f) < p+1/2. Applying the Franklin-Strömberg wavelet p = 1, we prove that the presented estimator of s*(f) is consistent for piecewise constant functions. Furthermore, we show that the results for the Franklin-Strömberg wavelet can be generalised to any spline wavelet (p ≥ 1).

Kategorie tematyczne

• 62G05: Estimation
• 41A35: Approximation by operators (in particular, by integral operators)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2013
• Tom: 40
• Numer: 3
• Strony: 309-326

Daty

wydano

2013

Twórcy

autor

Magdalena Meller

• Faculty of Applied Mathematics, Technical University of Gdańsk, G. Narutowicza 11/12, 80-952 Gdańsk, Poland

autor

Natalia Jarzębkowska

• Faculty of Applied Mathematics, Technical University of Gdańsk, G. Narutowicza 11/12, 80-952 Gdańsk, Poland

Identyfikatory

DOI

10.4064/am40-3-4