Unified approach to trimmed mean estimation and its application to bispectrum estimation of EEG signals

The trimmed mean estimator truncates both sides of the probability distribution by the same amount. For asymmetric distributions one needs to truncate the distribution on the left and right tails by different amounts which depend on the detailed properties—like the length of tails and asymmetry—of probability distributions. An adaptive generalised trimmed mean estimator for unimodal distributions is developed here to provide a unified approach to trimmed mean estimation. As realisations of different random processes vary very much in length of tails and asymmetry, an asymmetric generalised Gaussian distribution that covers a wide range of tails and asymmetry is employed to approximate the distributions of discrete data. Using this distribution, truncation points of the discrete distribution on both sides have been obtained. The adaptive generalised trimmed mean estimator is employed to estimate the autocorrelations and the third-order cumulants of simulated signals from various distributions as well as output signals from MA and ARMA systems. Finally the algorithm is applied to the bispectral analysis of event-related EEG-signals.