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Considerable eeort has been directed recently to develop asymptotically mini-max methods in problems of recovering innnite-dimensional objects (curves, densities , spectral densities, images) from noisy data. A rich and complex body of work has evolved, with nearly-or exactly-minimax estimators being obtained for a variety of interesting problems.(More)
Usually, methods for thresholding wavelet estimators are implemented term by term, with empirical coecients included or excluded depending on whether their absolute values exceed a level that re¯ects plausible moderate deviations of the noise. We argue that performance may be improved by pooling coecients into groups and thresholding them together. This(More)
In honor of Steve Smale's 75-th birthday with the warmest regards of the authors Abstract Let ρ be an unknown Borel measure defined on the space Z := X × Y with X ⊂ IR d and Y = [−M, M ]. Given a set z of m samples z i = (x i , y i) drawn according to ρ, the problem of estimating a regression function f ρ using these samples is considered. The main focus is(More)
a r t i c l e i n f o a b s t r a c t We consider the problem of recovering of continuous multi-dimensional functions f from the noisy observations over the regular grid m −1 Z d , m ∈ N *. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear filter, which can depend on the unknown function itself. In(More)
Density estimation is a commonly used test case for non-parametric estimation methods. We explore the asymptotic properties of estimators based on thresholding of empirical wavelet coecients. Minimax rates of convergence are studied over a large range of Besov function classes B s;p;q and for a range of global L 0 p error measures, 1 p 0 < 1. A single(More)
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