## Zbigniew Leonowicz, Juha Karvanen and Sergei L. Shishkin

## Trimmed estimators for robust averaging of event-related potentials

Averaging (in statistical terms, estimation of the location of data) is one of the most commonly used procedures in neuroscience and the basic procedure for obtaining event-related potentials (ERP). Only the arithmetic mean is routinely used in the current practice of ERP research, though its sensitivity to outliers is well-known. Weighted averaging is sometimes used as a more robust procedure, however, it can be not sufficiently appropriate when the signal is nonstationary within a trial. Trimmed estimators provide an alternative way to average data. In this paper, a number of such location estimators (trimmed mean, Winsorized mean and recently introduced trimmed L-mean) are reviewed, as well as arithmetic mean and median. A new robust location estimator tanh, which allows the data-dependent optimization, is proposed for averaging of small number of trials. The possibilities to improve signal-to-noise ratio (SNR) of averaged waveforms using trimmed location estimators are demonstrated for epochs randomly drawn from a set of real auditory evoked potential data.Keywords: Averaging; Event-related potentials; Evoked potentials; Mean; Median; Trimmed mean; Robust estimators of location; Trimmed estimators