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 AA-estimator, but also propose a new estimator based on the Student’s tt-distribution, which attains an efficiency close to that of the AA-estimator. We investigate the use of more efficient auxiliary location and scale estimators in two-pass estimators such as the AA- and tt-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.