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Biometrika 1977 64(1):79-84; doi:10.1093/biomet/64.1.79
© 1977 by Biometrika Trust
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Some Bayesian considerations in spectral estimation

PAUL SHAMAN

Department of Statistics, Carnegie-Mellon University Pittsburgh, Pennsylvania

This paper considers the problem of incorporating prior information about the shape and smoothness of a specrtal density into the formation of a spectral estimate. Two types of finite dimensional parameters are considered, the spectral ordinates at a specified collection of frequencies and the amount of power in each of a set of frequency bands. A method which is conditional on the .asymptotic distribution of periodogram averages is proposed. A formal procedure applies Bayes's theorem. A conjugate prior distribution is a product of inverted gamma, distributions. The results extend to estimation of a spectral density matrix in the vector case.

Key Words: Frequency band • Inverted gamma distribution • Periodogram • Prior distribution • Spectral density • Smoothing


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