A Measure Of Relative Efficiency For Location Of A Single Sample

Abstract

The question o f how much to trim or which weighting constant to use are practical considerations in applying robust methods such as trimmed means (L-estimators) and Huber statistics (M-estimators). An index o f location relative efficiency (LRE), which is a ratio of the narrowness o f resulting confidence intervals, was applied to various trimmed means and Huber M-estimators calculated on seven representative data sets from applied education and psychology research. On the basis of LREs, lightly trimmed means were found to be more efficient than heavily trimmed means, but Huber M-estimators systematically produced narrower confidence intervals. The weighting constant o f \j/ = 1.28 was found to be superior to various competitors suggested in the literature for n < 50.