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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

8,068 985- PDF

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

7,461 692- PDF

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

4,520 436- PDF

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

1,597 190- PDF

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

392 94- PDF

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

981 93- PDF

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

653 77- PDF

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

1,579 76- PDF

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

759 67- PDF

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

415 59- PDF

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