Confidence Intervals for Regression (MEM) Spectral Estimates.

摘要

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. The scaling of the spectral estimate, which is the estimate of the prediction error, is statistically independent of the estimated transfer function and has a Chi square distribution. Confidence intervals are calculated for an example consisting of several closely spaced tones in a background of white noise. These intervals are compared with those for the Maximum Likelihood Method. Generalizations are introduced for frequency wave number spectral estimation and for the joint density at different frequencies.