With ideal spatial adaptation, an oracle furnishes information about how best to adapt a spatially variable estimator, whether piecewise constant, piecewise polynomial, variable knot spline, orâ€¦ (More)

We attempt to recover a function of unknown smoothness from noisy, sampled data. We introduce a procedure, SureShrink, which suppresses noise by thresholding the empirical wavelet coe cients. Theâ€¦ (More)

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) fromâ€¦ (More)

We attempt to recover an unknown function from noisy, sampled data. Using orthonormal bases of compactly supported wavelets we develop a nonlinear method which works in the wavelet domain by simpleâ€¦ (More)

An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability atâ€¦ (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.â€¦ (More)

This paper explores a class of empirical Bayes methods for leveldependent threshold selection in wavelet shrinkage. The prior considered for each wavelet coefficient is a mixture of an atom ofâ€¦ (More)

Principal components analysis (PCA) is a classic method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. Contemporary datasets oftenâ€¦ (More)

Consider estimating the mean vector from data Nn( ; I) with lq norm loss, q 1, when is known to lie in an n-dimensional lp ball, p 2 (0;1). For large n, the ratio of minimax linear risk to minimaxâ€¦ (More)

Suppose we have observations yi = si+zi, i = 1; :::; n, where (si) is signal and (zi) is i.i.d. Gaussian white noise. Suppose we have available a library L of orthogonal bases, such as the Waveletâ€¦ (More)