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In this paper, we present an inverse estimation procedure which combines Fourier analysis with wavelet expansion. In the periodic setting, our method can recover a blurred function observed in white… (More)

- Albert Cohen, Ronald A. DeVore, Gerard Kerkyacharian, Dominique PicardJune
- 1999

In recent years, various nonlinear methods have been proposed and deeply investigated in the context of nonparametric estimation: shrinkage methods [21], locally adaptive bandwidth selection [16] and… (More)

We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in… (More)

We consider the problem of estimating an unknown function f in a regression setting with random design. Instead of expanding the function on a regular wavelet basis, we expand it on the basis… (More)

Let ρ be an unknown Borel measure defined on the space Z := X × Y with X ⊂ IR and Y = [−M,M ]. Given a set z of m samples zi = (xi, yi) drawn according to ρ, the problem of estimating a regression… (More)

We discuss a method for curve estimation based on n noisy data; one translates the empirical wavelet coe cients towards the origin by an amount p 2 log(n) = p n. The method is nearly minimax for a… (More)

- Domenico Marinucci, Davide Pietrobon, +6 authors Nicola Vittorio
- 2008

We discuss Spherical Needlets and their properties. Needlets are a form of spherical wavelets which do not rely on any kind of tangent plane approximation and enjoy good localization properties in… (More)

Constructing a good approximation to a function of many variables suffers from the “curse of dimensionality”. Namely, functions on R with smoothness of order s can in general be captured with… (More)

- T. Coulhon, Gerard Kerkyacharian, Pencho Petrushev
- 2012

Wavelet bases and frames consisting of band limited functions of nearly exponential localization on R are a powerful tool in harmonic analysis by making various spaces of functions and distributions… (More)

- Peter Hall, Spiridon I. Penev, Gerard Kerkyacharian, Dominique Picard
- Statistics and Computing
- 1997

PETER HALL, SPIRIDON PENEV, GEÂ RARD KERKYACHARIAN and DOMINIQUE PICARD Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia School of… (More)