Flexible empirical Bayes estimation for wavelets

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 Bayes (EB)...

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Veröffentlicht in:Journal of the Royal Statistical Society. Series B, Statistical methodology Statistical methodology, 2000, Vol.62 (4), p.681-698
Hauptverfasser: Clyde, Merlise, George, Edward I.
Format: Artikel
Sprache:eng
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Zusammenfassung: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 Bayes (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.
ISSN:1369-7412
1467-9868
DOI:10.1111/1467-9868.00257