Robust estimation of third-order cumulants in applications of higher-order statistics

A number of robust estimation of location algorithms are employed to estimate the third order cumulants of various lags from simulated signals representing the zero mean triangular, uniform and Gaussian distributions (as examples of symmetric distributions). Similar simulations have been performed on the output of AR, MA and ARMA systems that are being driven with random Gaussian input. Results appear to suggest that the (median), (weighted) biweight, and (weighted) wave estimators provide cumulant estimates consistent with expectations and of less variance than the mean estimator. This solves the problem with regard to symmetric distributions as these robust estimators have been designed for symmetric distributions. When these are applied to contaminated and asymmetric distributions (weighted) biweight and (weighted) wave estimators appear to give encouraging results. For asymmetric probability distributions, the various location parameters like the mean, median etc. are different, and further work with the particular emphasis on the estimation from asymmetric distributions is needed