A comparison of some univariate estimators in the presence of outliers

Abstract

In this study, sample mean, sample median and trimmed mean are compared in the presence of outliers through simulation study. Data used for this study are generated from R software under different cases. MSE and bias were used as statistical criterion. It has been observed and investigated from this study that the sample mean x was over used, in the sense that practitioner used it, even when the underlying distribution of data set at hand does not have normal distribution. Besides, using sample mean x, when normality assumption is violated, has been established from this study that variance obtained is usually large and the consequence of this is that it leads to imprecise estimate and poor statistical inference. In conclusion, this study suggests using 10% trimmed mean in the presence of outliers as against sample mean x.