Showing papers by "Iain M. Johnstone published in 1994"

Effects of intensive multiple risk factor reduction on coronary atherosclerosis and clinical cardiac events in men and women with coronary artery disease. The Stanford Coronary Risk Intervention Project (SCRIP).

Abstract: BACKGROUNDRecent clinical trials have shown that modification of plasma lipoprotein concentrations can favorably alter progression of coronary atherosclerosis, but no data exist on the effects of a...

Ideal denoising in an orthonormal basis chosen from a library of bases

Abstract: Nous decrivons une extension de la methode de la «meilleure base» qui permet de selectionner, a partir de donnees bruitees, une base orthonormee dans laquelle le debruitage est d'efficacite presque ideale

The Anatomy of the Posterior Communicating Artery as a Risk Factor for Ischemic Cerebral Infarction

Abstract: Background After the occlusion of an internal carotid artery the principal source of collateral flow is through the arteries of the circle of Willis, but the size and patency of these arteries are quite variable. Study of the anatomy of the collateral pathways in patients with internal-carotid-artery occlusion with or without infarction in the watershed area of the deep white matter may identify patterns that afford protection from ischemic infarction. Methods Using conventional magnetic resonance imaging and three-dimensional phase-contrast magnetic resonance angiography, we evaluated 29 consecutive patients (32 hemispheres at risk) with angiographically proved occlusion of the internal carotid artery. Four collateral pathways to the occluded vessel were evaluated: the proximal segment of the anterior cerebral artery, the posterior communicating artery, the ophthalmic artery, and leptomeningeal collateral vessels from the posterior cerebral artery. Results Only features of the ipsilateral posterior commu...

Threshold selection for wavelet shrinkage of noisy data

Abstract: Methods based on thresholding and shrinking empirical wavelet coefficients hold promise for recovering and/or denoising signals observed in noise. Here the authors review and compare various proposals for the choice of thresholds. These include soft and hard thresholding, and thresholds that are fixed in advance or chosen level by level from an empirical optimality criterion. The authors present results from simulations and real data examples. >

Minimax risk over l p -balls for l p -error

Abstract: Consider estimating the mean vector θ from dataN n (θ,σ 2 I) withl q norm loss,q≧1, when θ is known to lie in ann-dimensionall p ball,p∈(0, ∞). For largen, the ratio of minimaxlinear risk to minimax risk can bearbitrarily large ifp

Minimax Bayes, Asymptotic Minimax and Sparse Wavelet Priors

Abstract: Pinsker (1980) gave a precise asymptotic evaluation of the minimax mean squared error of estimation of a signal in Gaussian noise when the signal is known a priori to lie in a compact ellipsoid in Hilbert space This ‘Minimax Bayes’ method can be applied to a variety of global non-parametric estimation settings with parameter spaces far from ellipsoidal For example it leads to a theory of exact asymptotic minimax estimation over norm balls in Besov and Triebel spaces using simple co-ordinatewise estimators and wavelet bases

On Minimax Estimation of a Sparse Normal Mean Vector

Abstract: Mallows has conjectured that among distributions which are Gaussian but for occasional contamination by additive noise, the one having least Fisher information has (two-sided) geometric contamination. A very similar problem arises in estimation of a nonnegative vector parameter in Gaussian white noise when it is known also that most [i.e., $(1 - \varepsilon)$] components are zero. We provide a partial asymptotic expansion of the minimax risk as $\varepsilon \rightarrow 0$. While the conjecture seems unlikely to be exactly true for finite $\varepsilon$, we verify it asymptotically up to the accuracy of the expansion. Numerical work suggests the expansion is accurate for $\varepsilon$ as large as 0.05. The best $l_1$-estimation rule is first- but not second-order minimax. The results bear on an earlier study of maximum entropy estimation and various questions in robustness and function estimation using wavelet bases.