We prove that Schilder's theorem, giving large deviations estimates for the Brownian motion multiplied by a small parameter, still holds with the sup-norm replaced by any Hölder norm with exponent. We produce examples which show that this is effectively a stronger result and, as an application,...

One can slightly modify the usual Lp differentiability constraints of Sobolev types on densities with the help of Besov norms. This has the advantage, using the wavelets characterization of Besov spaces, to reduce the question of density estimation with Besov constraints to a problem in a...

Deconvolution problems are naturally represented in the Fourier domain, whereas thresholding in wavelet bases is known to have broad adaptivity properties. We study a method which combines both fast Fourier and fast wavelet transforms and can recover a blurred function observed in white noise...

This paper is showing that the saturation space of the minimax rate associated to a Lp loss and linear estimators is the Besov space Bs[infinity]p. More precisely, it is shown that if a function space included in Lp is such that its minimax rate is the usual one s/(1 + 2s) and if this rate is...

The extent to which wavelet function estimators achieve benchmark levels of performance is sometimes described in terms of our ability to interpret a mythical oracle, who has access to the "truth" about the target function. Since he is so wise, he is able to threshold in an optimal manner - that...