Flexible empirical Bayes estimation for wavelets
Flexible empirical Bayes estimation for wavelets
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DOI：
10.1111/1467-9868.00257
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发表时间：
2000-01-01
影响因子：
5.8
通讯作者：
George, EI
中科院分区：
文献类型：
--
作者：
Clyde, M;George, EI
小波收缩估计是一种越来越流行的信号去噪和压缩方法。尽管贝叶斯估计器可以提供出色的均方误差 (MSE) 属性，但选择有效的先验是一项艰巨的任务。为了解决这个问题，我们提出了针对各种误差分布（包括正态分布和重尾学生 t 分布）的经验保存 (EB) 先验选择方法。在这种 EB 先验分布下，我们获得基于模型选择的阈值收缩估计器和基于模型平均的多重收缩估计器。这些 EB 估计器在计算上与标准经典阈值方法相比具有竞争力，并且对数据和小波域中的异常值具有鲁棒性。模拟和真实示例用于说明这些方法在各种设置中的灵活性和改进的 MSE 性能。
Wavelet shrinkage estimation is an increasingly popular method for signal denoising and compression. Although Bayes estimators can provide excellent mean-squared error (MSE) properties, the selection of an effective prior is a difficult task. To address this problem, we propose empirical Saves (EB) prior selection methods for various error distributions including the normal and the heavier-tailed Student t-distributions. Under such EB prior distributions, we obtain threshold shrinkage estimators based on model selection, and multiple-shrinkage estimators based on model averaging. These EB estimators are seen to be computationally competitive with standard classical thresholding methods, and to be robust to outliers in both the data and wavelet domains. Simulated and real examples are used to illustrate the flexibility and improved MSE performance of these methods in a wide variety of settings.