Higher order statistics (HOS) in signal processing are they of any use?

The general motivation behind the use of higher order spectra in signal processing is threefold: (1) to extract information due to deviations from Guassianity, (2) to estimate the phase of non-Gaussian parametric signals, and (3) to detect and characterise the nonlinear properties of mechanisms which generate time series via phase relations of their harmonic components. The objective of this paper is twofold: first, in attempting to perform the difficult task of providing fair and useful answers to the question title against various conflicting figures of merit associated with (HOS) based digital signal processing, the paper draws some useful conclusions based on (a) some carefully selected results published in learned journals and national/internationaI conferences (1990-95), and (b) our own experience(s) in areas such as that concerning the applications of HOS to testing for nonlinearity due to chromatic aberration in white light interferometric systems operating under the influence of Gaussian noise and the utilisation of HOS to classify/diagnose or even deconvolute two ECG Signals