I. Johnstone
- Publications
- Influence
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SUMMARY 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,… Expand
Abstract We attempt to recover a function of unknown smoothness from noisy sampled data. We introduce a procedure, SureShrink, that suppresses noise by thresholding the empirical wavelet… Expand
Let x (1) denote the square of the largest singular value of an n x p matrix X, all of whose entries are independent standard Gaussian variates. Equivalently, x (1) is the largest principal component… Expand
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 at… Expand
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 simple… Expand
Density estimation is a commonly used test case for nonparametric estimation methods. We explore the asymptotic properties of estimators based on thresholding of empirical wavelet coefficients.… Expand
Much recent effort has sought asymptotically minimax methods for recovering infinite dimensional objects-curves, densities, spectral densities, images-from noisy data. A now rich and complex body of… Expand
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 often… Expand
We attempt to recover an n-dimensional vector observed in white noise, where n is large and the vector is known to be sparse, but the degree of sparsity is unknown. We consider three different ways… Expand