Confidence intervals for regression (MEM) spectral estimates

The probability density and confidence intervals for the maximum entropy (or regression) method (MEM) of spectral estimation are derived using a Wishart model for the estimated covariance. It is found that the density for the estimated transfer function of the regression filter may be interpreted as a generalization of the student's t distribution. Asymptotic expressions are derived which are the same as those of Akaike. These expressions allow a direct comparison between the performance of the maximum entropy (regression) and maximum likelihood methods under these asymptotic conditions. Confidence intervals are calculated for an example consisting of several closely space tones in a background of white noise. These intervals are compared with those for the maximum likelihood method (MLM). It is demonstrated that, although the MEM has higher peak to background ratios than the MLM, the confidence intervals are correspondingly larger. Generalizations are introduced for frequency wavenumber spectral estimation and for the joint density at different frequencies.