Robust Estimation in the Presence of Outliers

Publisher Summary This chapter discusses the bias and mean square error of various estimators of location and scale in the presence of an unidentified outlier. Publications on robust estimation sometimes convey the impression that tests for outliers are irrelevant. The argument seems to be that robust estimators are constructed to perform reasonably well as long as the number of outliers is not too large. The more extreme observations in the sample are typically given little or no weight in the robust estimator. Moreover, the argument proceeds, those observations that are rejected by some standard test for outliers may not be outliers at all; rather, the case may be of a long-tailed distribution. It is important, therefore, to reiterate another aim of outlier tests, crucial in the proper treatment of data, namely, the identification of observations deserving closer scrutiny. It is sometimes suggested that outlier tests be performed at the 10% or even 20% level. Raising the significance level will certainly improve the robustness of estimators based on the surviving observations.