Bayesian Decision Theoretic Scale-Adaptive Estimation of a Log-Spectral Density

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Pensky, Marianna
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Wallace H. Coulter Department of Biomedical Engineering
The joint Georgia Tech and Emory department was established in 1997
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http://hdl.handle.net/1853/25912
Abstract
The problem of estimating the log-spectrum of a stationary Gaussian time series by Bayesianly induced shrinkage of empirical wavelet coefficients is studied. A model in the wavelet domain that accounts for distributional properties of the log-periodogram at levels of fine detail and approximate normality at coarse levels in the wavelet decomposition, is proposed. The smoothing procedure, called BAMS-LP (Bayesian Adaptive Multiscale Shrinker of Log-Periodogram), ensures that the reconstructed log-spectrum is as noise-free as possible. It is also shown that the resulting Bayes estimators are asymptotically optimal (in the frequentist sense). Comparisons with non-wavelet and wavelet-non-Bayesian methods are discussed.
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2003
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Technical Report
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