Multiple Window Bispectrum Estimator

By taking the third-order statistical information of processes into account, the bispectrum is a useful tool in digital signal processing and statistics. The paper proposes a nonparametric approach of estimating the bispectrum, using tapers designed to achieve maximal bifrequency concentration. Bispectra are functions of two frequencies plus their sum, so the optimum tapers are not products of Slepian sequences. The new tapers minimize the sixth-moment "energy" leakage in the estimate, and thus the new multiple window bispectrum estimator (MWBE) can be interpreted as minimizing the broad-band bias. Alternatively, the MWBE can be viewed as a solution of an integral inverse problem using an eigenfunction expansion. This approach can be extended to estimate higher-order polyspectra. Numerical simulations use moving average (MA) data with non-Gaussian white driving noise. Simulation results with small sample sizes show that this new MWBE is feasible and mean-squared error (MSE) optimal