Do Robust Estimators Work with Real Data?

Most studies of robust estimators of location parameters have relied upon mathematical theory, computer simulated data, or a combination of these. This paper presents a comparison of the performances of eleven estimators using real data sets. Twenty sets of data from 1761 determinations of the parallax of the sun, from 1798 measurements of the mean density of the earth, and from circa 1880 measurements of the speed of light, are employed in the study, with the current values of these physical constants being compared with the estimators' realized values. We find that light trimming provides some improvement over the sample mean, but that the sample mean itself compares favorably with many recent proposals. The bias and nonnormality of the data sets is considered, and the data sets are presented and discussed in an appendix.