Premium
Flexible empirical Bayes estimation for wavelets
Author(s) -
Clyde Merlise,
George Edward I.
Publication year - 2000
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00257
Subject(s) - estimator , shrinkage estimator , wavelet , mean squared error , bayes' theorem , outlier , shrinkage , mathematics , statistics , computer science , thresholding , prior probability , selection (genetic algorithm) , pattern recognition (psychology) , artificial intelligence , algorithm , bayesian probability , minimax estimator , image (mathematics) , minimum variance unbiased estimator
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.