Confidence regions for spectral bounds

Existing variance calculations for spectral estimates are unsatisfactory in that they depend upon information that is usually unavailable in practice. Some recent work in spectral estimation has involved the computation of bounds on the average spectral density in some region from a true correlation matrix. The computation of these bounds involves optimization over a set of spectra that are consistent with the correlation matrix. The specific new work to be reported on involves the construction of confidence regions for the true correlation matrix, based on a Wishart distributed sample correlation matrix. Bounds computed over spectra that are consistent with the true correlation matrix being in this set are valid with a certain minimum a priori probability which does not depend upon unavailable information about the spectrum. The result is a performance characterization for the bounding method which is different and, in some ways, more satisfactory than the existing variance analyses for other spectral estimation methods.