A reinvestigation of robust scale estimation in finite samples

This paper reworks and expands on the results of existing simulation studies, investigating the performance of various robust estimators of scale for Tukey’s three corner distributions. We focus attention on the popular biweight A-estimator, but also propose a new estimator based on the Student’s t-distribution, which attains efficiency close to that of the A-estimator. We investigate use of more efficient auxiliary location and scale estimators in the two-pass estimators such as the Aand t-estimators, and find overall efficiency can be improved. Using much larger simulation sizes than previous studies, significant departures from existing efficiencies are obtained, and these lead to different recommendations for estimation.