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April, 1969 Phase Free Estimation of Coherence
Richard H. Jones
Ann. Math. Statist. 40(2): 540-548 (April, 1969). DOI: 10.1214/aoms/1177697722


A phase free estimate of the coherence of a bivariate Gaussian process is presented. The technique is based on the usual independent, complex normal approximation to the distribution of the finite Fourier transform of a multivariate stationary time series, and the complex Wishart approximation to the distribution of spectrum estimates. If the spectral densities and coherence can be assumed to be constant over a wider frequency band than the phase can be assumed to be constant, the concept of inner and outer spectral windows would seem appropriate. Maximum likelihood estimates of the coherence are obtained using phase free marginal distributions at the inner window level. The results of simulations are presented showing the likelihood for various inner windows.


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Richard H. Jones. "Phase Free Estimation of Coherence." Ann. Math. Statist. 40 (2) 540 - 548, April, 1969.


Published: April, 1969
First available in Project Euclid: 27 April 2007

zbMATH: 0174.22001
MathSciNet: MR239711
Digital Object Identifier: 10.1214/aoms/1177697722

Rights: Copyright © 1969 Institute of Mathematical Statistics

Vol.40 • No. 2 • April, 1969
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