Iain M. Johnstone

Least angle regression

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 whi...

Ideal Spatial Adaptation by Wavelet Shrinkage

Journal Article Ideal spatial adaptation by wavelet shrinkage Get access David L Donoho, David L Donoho Department of Statistics, Stanford University, Stanford, California, U.S....

Adapting to Unknown Smoothness via Wavelet Shrinkage

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 empirica...

Minimax estimation via wavelet shrinkage

We attempt to recover an unknown function from noisy, sampled data.\nUsing orthonormal bases of compactly supported wavelets, we develop a nonlinear\nmethod which works in the w...

Empirical Functionals and Efficient Smoothing Parameter Selection

SUMMARY A striking feature of curve estimation is that the smoothing parameter ĥ 0, which minimizes the squared error of a kernel or smoothing spline estimator, is very difficul...

Ideal spatial adaptation by wavelet shrinkage

SUMMARY With ideal spatial adaptation, an oracle furnishes information about how best to adapt a spatially variable estimator, whether piecewise constant, piecewise polynomial, ...

Adapting to unknown sparsity by controlling the false discovery rate

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 ...

Minimax risk overl p -balls forl p -error

Exact Risk Analysis of Wavelet Regression

Abstract Wavelets have motivated development of a host of new ideas in nonparametric regression smoothing. Here we apply the too] of exact risk analysis, to understand the small...

Exact Risk Analysis of Wavelet Regression

Wavelet Shrinkage: Asymptopia?

SUMMARY Much recent effort has sought asymptotically minimax methods for recovering infinite dimensional objects—curves, densities, spectral densities, images—from noisy data. A...

On Consistency and Sparsity for Principal Components Analysis in High Dimensions

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. Contem...

Minimax bounds for sparse PCA with noisy high-dimensional data

We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish a lower b...

Projection-Based Approximation and a Duality with Kernel Methods

Projection pursuit regression and kernel regression are methods for estimating a smooth function of several variables from noisy data obtained at scattered sites. Methods based ...