WaveShrink: Shrinkage Functions and Thresholds

Donoho and Johnstone's WaveShrink procedure has proven valuable for signal de-noising and non-parametric regression. WaveShrink is based on the principle of shrinking wavelet coefficients towards zero to remove noise. WaveShrink has very broad asymptotic near-optimality properties. In this paper, we introduce a new shrinkage scheme, semisoft, which generalizes hard and soft shrinkage. We study the properties of the shrinkage functions, and demonstrate that semisoft shrinkage offers advantages over both hard shrinkage (uniformly smaller risk and less sensitivity to small perturbations in the data) and soft shrinkage (smaller bias and overall L 2 risk). We also construct approximate pointwise confidence intervals for WaveShrink and address the problem of threshold selection. Key Words: WaveShrink; Bias Estimation; Confidence Interval; Minimax Thresholds; Non-parametric Regression; Semi-Soft Shrinkage; Signal De-noising; Variance Estimation; Wavelet Transform; 1 INTRODUCTION Suppose we ..