Minimum Cross-Entropy Spectral Analysis.
NAVAL RESEARCH LAB WASHINGTON D C
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The principle of minimum cross-entropy minimum directed divergence is summarized, discussed, and applied to the classical problem of estimating power spectra given samples of the autocorrelation function. This new approach reduces to maximum entropy spectral analysis MESA in certain special cases, and thereby provides a fundamental derivation of MESA. In contrast to MESA, the minimum cross-entropy approach makes use of prior information about the power spectrum. Depending on the extent of prior information, various alternative minimum cross-entropy spectral estimates are obtained. When a prior estimate of the power spectrum is available, the minimum cross-entropy result differs from the MESA result. Results are derived in two equivalent ways once by minimizing the cross-entropy of underlying probability densities, and once by arguments concerning the cross-entropy between the input and output of linear filters.
- Statistics and Probability