Considerable e ort has been directed recently to develop asymptotically minimax methods in problems of recovering in nite-dimensional objects (curves, densities, spectral densities, images) from… (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 coe cients.… (More)

We consider a sequence space model of statistical linear inverse problems where we need to estimate a function f from indirect noisy observations. Let a nite set of linear estimators be given. Our… (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)

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 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)

Block thresholding methods have been proposed by Hall, Kerkyacharian and Picard (1995) as a means of obtaining increased adaptivity when estimating a function using wavelet methods. For example, it… (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)

Article history: Received 29 July 2008 Revised 29 May 2009 Accepted 3 June 2009 Available online 12 June 2009 Communicated by W.R. Madych A linear method for inverting noisy observations of the Radon… (More)

Let X1, . . . , Xn be a random sample from some unknown probability density f defined on a compact homogeneous manifold M of dimension d ≥ 1. Consider a ‘needlet frame’ {φ jη} describing a localised… (More)