Locally Adaptive Tree-Based Thresholding

Evers, L. and Heaton, T. J. (2009) Locally Adaptive Tree-Based Thresholding. Journal of Computational and Graphical Statistics, 18(4), pp. 961-977. (doi: 10.1198/jcgs.2009.07109)

Abstract

This article is concerned with the application of thresholding to the estimation of possibly sparse single sequence data observed subject to noise. In Such problems, accuracy can be greatly improved by selecting a threshold that adapts to the unknown signal strength. We set out a classification and regression tree approach aimed at partitioning a sequence of inhomogeneous strength into component homogeneous regions where we call independently set a locally adaptive threshold and thus improve estimation. Our method places a mixture prior oil each coefficient consisting of all atom of probability at zero and a symmetric probability density. The mixing weight is chosen via Empirical Bayes. The decision on whether a split should occur is based on a score test. Having selected the partitioning and obtained the local mixing weight for each region, estimation is carried out using the posterior median. We evaluate the performance Of Our method in the single sequence case and for wavelet denoising on both simulated and real data. In the wavelet context we consider two alternative implementations, splitting the coefficients levelwise and splitting the original domain. Our method is cheap to compute and in numerical comparisons our method shows excellent performance when compared with current thresholding techniques. This article has supplementary material online

• Item Type: Articles
• Keywords: BAYES Classification Classification and regression tree Empirical Bayes REGRESSION SEQUENCE Sparsity STRENGTH Wavelet denoising
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Evers, Dr Ludger
• Authors: Evers, L., and Heaton, T. J.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Journal Name: Journal of Computational and Graphical Statistics
• ISSN: 1061-8600