On the robust estimation of cumulants

Abstract

Robust estimation of location algorithms are employed to estimate the third order cumulants of various lags from simulated signals representing the zero mean Uniform and Gaussian distributions (as examples of symmetric distributions). It is demonstrated that the biweight, wave, and median estimators provide consistent cumulant estimates of less variance than the (most common) mean estimator. This solves the problem with regard to symmetric distributions as these robust estimators have been designed for symmetric distribution. When these are applied to asymmetric distributions, biweight and wave estimators appear to give encouraging results. Further work with the particular emphasis on the estimation from asymmetric distributions is under way.<>