Norm Thresholding Method in Wavelet Regression

ISSN： 0094-9655

Source： Journal of Statistical Computation and Simulation, Vol.72, Iss.3, 2002-01, pp. : 233-245

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Abstract

In this paper we present a new method called the NORM method for finding threshold values in wavelet regression. We use WaveThresh (G. Nason) software in S-Plus to implement this method, and compare it with existing methods, such as Donoho and Johnstone's SureShrink, AdaptShrink and Nason's cross-validation, and with optimal thresholding. The goal is to minimize the average mean-squared error. We use 3 different kinds of noise: iid normal, iid t variable, and correlated noise, on 8 different test applications. For iid normal noise, any method could be the best. The cross-validation method works best for independent long-tailed t noise. In the case of correlated noise, the NORM method behaves best when there is a large, positive lag one correlation. The SureShrink or AdaptShrink methods behave best when there is a large, negative lag one correlation. We give heuristic explanations of these behaviors. We also evaluate the accuracy of our method for estimation of noise level sigma .