In many regression settings the unknown coefficients may have some known structure, for instance they be ordered in space or correspond to a vectorized matrix tensor. At same time, sparse, with nearly exactly equal zero. However, commonly used priors and corresponding penalties do not encourage simultaneously structured sparse estimates. this paper we develop shrinkage that generalize multivari...

Shrinkage of concrete, along with the cracking that often accompanies it, has been a continual concern of the concrete construction community.1,2 In the past 20 years or so, numerous shrinkage-reducing admixtures (SRAs) have been developed with the goal of reducing drying shrinkage and delaying or preventing cracking.2-6 Most SRAs function by reducing the surface tension of the pore solution in...

This paper builds on a simple unified representation of shrinkage Bayes estimators based on hierarchical Normal-Gamma priors. Various popular penalized least squares estimators for shrinkage and selection in regression models can be recovered using this single hierarchical Bayes formulation. Using 129 U.S. macroeconomic quarterly variables for the period 1959 – 2010 I exhaustively evaluate the ...

Biased regression is an alternative to ordinary least squares (OLS) regression, especially when explanatory variables are highly correlated. In this paper, we examine the geometrical structure of the shrinkage factors of biased estimators. We show that, in most cases, shrinkage factors cannot belong to [0, 1] in all directions. We also compare the shrinkage factors of ridge regression (RR), pri...

The relation of soft wavelet shrinkage (Donohoshrinkage) and variational denoising was discovered by Chambolle, Lucier et al. [3, 4]. Here we present an outline of this relation and give a non-convex generalization which will be related to hard wavelet shrinkage. This approach will lead to a “natural” interpolation between soft and hard shrinkage. AMS Subject Classification: 65K10, 42C40

Most two-dimensional methods for wavelet shrinkage are efficient for edge-preserving image denoising, but they suffer from poor rotation invariance. We address this problem by designing novel shrinkage rules that are derived from rotationally invariant nonlinear diffusion filters. The resulting Haar wavelet shrinkage methods are computationally inexpensive and they offer substantially improved ...