Wavelet threshold estimators for data with correlated noise
Wavelet threshold estimators for data with correlated noise
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DOI：
10.1111/1467-9868.00071
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发表时间：
1997-01-01
影响因子：
5.8
通讯作者：
Silverman, BW
中科院分区：
文献类型：
--
作者：
Johnstone, IM;Silverman, BW
通过对小波变换中的系数应用依赖于电平的软阈值来构造具有平稳相关噪声的数据的小波阈值估计器。提出了多种阈值选择，包括基于均方误差无偏估计的阈值选择。该方法的实际性能通过示例进行了演示，包括来自神经生理学背景的数据。通过将估计量与理想但无法实现的“基准”进行比较来研究估计量的理论特性，“基准”可以在小波背景下被视为通过理想空间适应性获得的风险，更一般地是通过使用提供数据中实际不可用信息的“预言机”来获得。结果表明，水平相关阈值估计器相对于基准风险表现良好，并且任何其他估计器都无法在数量级上改进其极小极大行为。考虑了短程和长程相关噪声的小波域结构，并且在这两种情况下都表明估计器在广泛的函数类中同时具有接近最优的行为，自动适应基础模型的规律性属性。主要结果的证明是通过考虑更一般的多元正态决策理论问题获得的。
Wavelet threshold estimators for data with stationary correlated noise are constructed by applying a level-dependent soft threshold to the coefficients in the wavelet transform. A variety of threshold choices is proposed, including one based on an unbiased estimate of mean-squared error. The practical performance of the method is demonstrated on examples, including data from a neurophysiological context. The theoretical properties of the estimators are investigated by comparing them with an ideal but unattainable 'bench-mark', that can be considered in the wavelet context as the risk obtained by ideal spatial adaptivity, and more generally is obtained by the use of an 'oracle' that provides information that is not actually available in the data. It is shown that the level-dependent threshold estimator performs well relative to the bench-mark risk, and that its minimax behaviour cannot be improved on in order of magnitude by any other estimator. The wavelet domain structure of both short- and long-range dependent noise is considered, and in both cases it is shown that the estimators have near optimal behaviour simultaneously in a wide range of function classes, adapting automatically to the regularity properties of the underlying model. The proofs of the main results are obtained by considering a more general multivariate normal decision theoretic problem.