Showing papers by "Iain M. Johnstone published in 2014"
01 Mar 2014
TL;DR: In this article, the linear inverse problem of estimating an unknown signal f from noisy measurements on Kf where the linear operator K admits a wavelet-vaguelette decomposition is considered.
Abstract: We consider the linear inverse problem of estimating an unknown signal f from noisy measurements on Kf where the linear operator K admits a wavelet–vaguelette decomposition. We formulate the problem in the Gaussian sequence model and propose estimation based on complexity penalized regression on a level-by-level basis. We adopt squared error loss and show that the estimator achieves exact rate-adaptive optimality as f varies over a wide range of the Besov function classes. Copyright © 2014 John Wiley & Sons, Ltd.
10 citations
01 Jan 2014
TL;DR: The classic superefficient estimate of Hodges for a one dimensional normal mean and the modern hard thresholding estimates introduced in the works of David Donoho and Iain Johnstone exhibit some well known risk phenomena.
Abstract: The classic superefficient estimate of Hodges for a one dimensional normal mean and the modern hard thresholding estimates introduced in the works of David Donoho and Iain Johnstone exhibit some well known risk phenomena. They provide quantifiable improvement over the MLE near zero, but also suffer from risk inflation suitably away from zero. Classic work of Le Cam and Hajek has precisely pinned down certain deep and fundamental aspects of these risk phenomena.
2 citations