Robust Alternatives to the Standard Deviation in Processing of Physics Experimental Data

Abstract

Properties of robust estimations of the scale parameter are studied. It is noted that the median of absolute deviations and the modified estimation of the average Gini differences have asymptotically normal distributions and bounded influence functions, are B-robust estimations, and hence, unlike the estimation of the standard deviation, are protected from the presence of outliers in the sample. Results of comparison of estimations of the scale parameter are given for a Gaussian model with contamination. An adaptive variant of the modified estimation of the average Gini differences is considered.