Norm thresholding method in wavelet regression
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.
wavelet regression norm method thresholding value sureshrink cross-validation optimal level-dependent