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- David L Donoho, Iain M Johnstone, G Erard Kerkyacharian, Dominique Picard
- 1995

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 coecients 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 coecients 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)

- David L Donoho, Iain M Johnstone, G Erard Kerkyacharian, Dominique Picard
- 1996

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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