Statistics of Sxy Estimates

M. H. Freilich Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109

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S. S. Pawka Center for Coastal Studies, Scripps Institution of Oceanography, La Jolla, CA 92093

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Abstract

The statistics of Sxy estimates derived from orthogonal-component measurements are examined. Based on results of Goodman, the probability density function (pdf) for Sxy(f) estimates is derived, and a closed-form solution for arbitrary moments of the distribution is obtained. Characteristic functions are used to derive the exact pdf of Sxytot. In practice, a simple Gaussian approximation is found to be highly accurate even for relatively few degrees of freedom. Implications for experiment design are discussed, and a maximum likelihood estimator for a posteriori estimation is outlined.

Abstract

The statistics of Sxy estimates derived from orthogonal-component measurements are examined. Based on results of Goodman, the probability density function (pdf) for Sxy(f) estimates is derived, and a closed-form solution for arbitrary moments of the distribution is obtained. Characteristic functions are used to derive the exact pdf of Sxytot. In practice, a simple Gaussian approximation is found to be highly accurate even for relatively few degrees of freedom. Implications for experiment design are discussed, and a maximum likelihood estimator for a posteriori estimation is outlined.

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