Statistics Seminar:: BAYESIAN DECISION THEORETIC SCALE-ADAPTIVE ESTIMATION OF A LOG-SPECTRAL DENSITY
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.
- Workflow Status: Published
- Created By: Barbara Christopher
- Created: 10/08/2010
- Modified By: Fletcher Moore
- Modified: 10/07/2016