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Statistics Seminar:: BAYESIAN DECISION THEORETIC SCALE-ADAPTIVE ESTIMATION OF A LOG-SPECTRAL DENSITY

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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.

This is a joint work with Marianna Pensky from UCF.

Status

  • Workflow Status: Published
  • Created By: Barbara Christopher
  • Created: 10/08/2010
  • Modified By: Fletcher Moore
  • Modified: 10/07/2016

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