Comparison of robust estimates of modified variants of standard deviations and average absolute deviations

Robust estimates of the scale parameter characterizing the spread of a random variable are studied in the present work. Estimates are proposed that are asymptotically normally distributed, have bounded influence functions, and hence, in contrast to the standard deviation estimate, are protected from the presence of outliers in the sample. The estimates are calculated based on order statistics from which a part of observations has been preliminarily removed. An adaptive version of the estimates based on the application of the sample estimates of functionals characterizing the length of the distribution tails is proposed. The results of comparing the estimates of the scale parameter for different observation models are presented. In particular, a Gaussian model with large-scale contamination is used to describe the presence of outliers in the sample