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Least angle regression
- B. Efron, T. Hastie, I. Johnstone, R. Tibshirani
- Mathematics
- 1 April 2004
The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be… Expand
Ideal spatial adaptation by wavelet shrinkage
- D. Donoho, I. Johnstone
- Mathematics
- 1 September 1994
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
Adapting to Unknown Smoothness via Wavelet Shrinkage
- D. Donoho, I. Johnstone
- Mathematics
- 1 December 1995
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
On the distribution of the largest eigenvalue in principal components analysis
- I. Johnstone
- Mathematics
- 1 April 2001
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
Needles and straw in haystacks: Empirical Bayes estimates of possibly sparse sequences
- I. Johnstone, B. Silverman
- Mathematics
- 1 August 2004
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
Minimax estimation via wavelet shrinkage
- D. Donoho, I. Johnstone
- Mathematics
- 1 June 1998
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
On Consistency and Sparsity for Principal Components Analysis in High Dimensions
- I. Johnstone, A. Lu
- Mathematics, Medicine
- Journal of the American Statistical Association
- 1 June 2009
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
Wavelet Shrinkage: Asymptopia?
- D. Donoho, I. Johnstone, G. Kerkyacharian, D. Picard
- Mathematics
- 1 July 1995
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
Density estimation by wavelet thresholding
- D. Donoho, I. Johnstone, G. Kerkyacharian, D. Picard
- Mathematics
- 1 April 1996
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
Adapting to unknown sparsity by controlling the false discovery rate
- Felix Abramovich, Y. Benjamini, D. Donoho, I. Johnstone
- Mathematics
- 18 May 2005
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
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