Bispectra and phase of non-Gaussian linear processes

Abstract

The phase of the transfer function of linear processes which cannot be identified in the Gaussian case can be almost fully resolved in the non-Gaussian case. Estimates have been proposed in the past. A nonparametric estimate of the phase with better asymptotic convergence properties as a function of sample size is studied here. The asymptotic behavior of the bias and variance of the estimate is examined. In particular the variance of the phase estimate is shown to be asymptotically independent of the frequency (if the frequency is not zero). Related problems are of interest in deconvolution, transfer function estimation, as well as in the resolution of astronomical images (perturbed by atmospheric turbulence) obtained by earth based telescopes.