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 σ .

Keywords:

• Wavelet Regression
• Thresholding Value
• Level-dependent
• Cross-validation
• Sureshrink
• Optimal
• Norm Method