Robust estimation of standard deviation

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Abstract
Six different estimators of standard deviation have been compared by stochastic simulations and by asymptotic calculations. The observations were independent, identically distributed either with a normal distribution or with a distribution in the “neighbourhood” of a normal distribution The simulations showed that the usual standard deviation estimator is too sensitive against deviations from normality, Estimators based on the absolute deviation or on a fractile-difference turned out to be better under the considered deviations from normality, and compared well with the usual estimator under normal assumptions The asymptotic calculations showed that comparing asymptotic values of two estimators may give a false impression of their corresponding finite properties

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