Multitaper estimators for bispectra

We have compared the bias and variance properties of a multitaper based class of bispectral estimators, with those of frequency smoothed biperiodograms, and a Hann-tapered/frequency-smoothed biperiodogram. The test processes are a white Gaussian process, a Poisson-driven MA(1) process, and a Poisson-driven AR(2) process. We found that the bias and variance properties of the mulitaper bispectral estimators are governed mainly by a quantity we call the total bispectral window. We conclude that for bispectra with a small dynamical range, the multitaper based estimators are superior, but for bispectra with a large dynamical range are the statistical properties of the Hann-tapered/frequency-smoothed estimator indistinguishable from those of the multitaper estimator.