Spectral estimation of continuous-time stationary processes from random sampling
Let X = {X(t), - [infinity] < t < [infinity]} be a continuous-time stationary process with spectral density function [phi]X([lambda]) and {[tau]k} be a stationary point process independent of X. Estimates of [phi]X([lambda]) based on the discrete-time observation {X([tau]k), [tau]k} are considered. Asymptotic expressions for the bias and covariance of are derived. A multivariate central limit theorem is established for the spectral estimators . Under mild conditions, it is shown that the bias is independent of the statistics of the sampling point process {[tau]k} and that there exist sampling point processes such that the asymptotic variance is uniformly smaller than that of a Poisson sampling scheme for all spectral densities [phi]X([lambda]) and all frequencies [lambda].
Year of publication: |
1994
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Authors: | Lii, Keh-Shin ; Masry, Elias |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 52.1994, 1, p. 39-64
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Publisher: |
Elsevier |
Keywords: | Spectral estimation of continuous-time processes Point processes Alias-free sampling Asymptotic bias Covariance Normality |
Saved in:
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