A COMPARISON OF OPTIMIZED HIGHER-ORDER SPECTRAL DETECTION TECHNIQUES FOR NON-GAUSSIAN SIGNALS

Using the Gaussian noise rejection property of higher order spectra (H OS), HOS-based detectors have been proposed that outperform convention al second-order techniques in certain scenarios. Based on statistical tests proposed by Subba Rao and Gabr, as well as Hinich, recently, Kle tter and Messer, and Hinich and Wilson, have developed similar bifrequ ency-domain detectors that are dependent on bispectral estimates of th e observation process. Formalizing the estimate consistency requiremen ts and the asymptotics for these detectors, we derive a new F-test sta tistic. We consider the detrimental effects of using spectral estimate s in the denominator of Hinich's test. We determine refined conditiona l distributions for third- and fourth-order versions of his detector. We also modify his test for colored scenarios, Extending the bispectra l detectors to their kth-order counterparts, we calculate the optimal smoothing bandwidth to use in constructing the HOS estimates, producin g the best detection performances for both our F-test and Hinich's tes t with our refined distributions. These new bandwidths yield significa nt improvements in detector performance over previous results. For the finite sample case, our calculations characterize the tradeoff betwee n the two detectors and demonstrate that a larger smoothing bandwidth than the one suggested by previous researchers should be used. Our cal culations are verified using simulations for both white and colored ca ses.