Robust M-Estimators Of The Population Mean

Abstract

Valuable information may be contained in outliers. Data collected from many medical equipment such as the ECG time-series may result in unusual patterns, a situation that may represent disease conditions. Some outliers may therefore provide an insight into crucial information that may lead to the discovery of new knowledge.Due to the diculties involved in the study of outliers, majority of current research works have chosen not to out-rightly reject the outliers but have adopted methods that accommodates them but have their inuence reduced to some degree. This has resulted in the development of estimation and testing techniques that have yielded robust estimation. Three robust M-estimators (the Huber, the Hampel and the Tukey's biweight) were adopted in this paper with an aim of comparing their eciency in the estimation of population mean in an asymmetrical distribution. Simulation was used to generate a normal population which was then contaminated with a few outlying observations. A simple example illustrated how the comparison of the M- estimators was carried out on real data. On the basis of the ndings from this research, the M-estimator that turned out to be the best, was the Tukey's biweight followed by the Hampel's and the Huber's was the weakest of the three. However all the three M-estimators yielded unbiased estimates of the population mean.