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Robust Wavelet Shrinkage Using Robust Selection Of Thresholds

机译：使用阈值的稳健选择进行稳健的小波收缩

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摘要

This paper considers the problem of selecting a robust threshold of wavelet shrinkage. Previous approaches reported in literature to handle the presence of outliers mainly focus on developing a robust procedure for a given threshold; this is related to solving a nontrivial optimization problem. The drawback of this approach is that the selection of a robust threshold, which is crucial for the resulting fit is ignored. This paper points out that the best fit can be achieved by a robust wavelet shrinkage with a robust threshold. We propose data-driven selection methods for a robust threshold. These approaches are based on a coupling of classical wavelet thresholding rules with pseudo data. The concept of pseudo data has influenced the implementation of the proposed methods, and provides a fast and efficient algorithm. Results from a simulation study and a real example demonstrate the promising empirical properties of the proposed approaches.
机译：本文考虑了选择鲁棒小波收缩阈值的问题。文献中报道的用于处理异常值的先前方法主要集中于针对给定阈值开发可靠的过程。这与解决非平凡的优化问题有关。这种方法的缺点是忽略了对于生成的拟合至关重要的稳健阈值的选择。本文指出，具有鲁棒阈值的鲁棒小波收缩可以实现最佳拟合。我们为稳健的阈值提出了数据驱动的选择方法。这些方法基于经典小波阈值规则与伪数据的耦合。伪数据的概念影响了所提出方法的实现，并提供了一种快速有效的算法。仿真研究和一个实际例子的结果证明了所提出方法的有希望的经验性质。

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