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Finite-sample Rousseeuw-Croux scale estimators
Andrey Akinshin
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The Rousseeuw-Croux Sₙ, Qₙ scale estimators and the median absolute deviation MADₙ can be used as consistent estimators for the standard deviation under normality. All of them are highly robust: the breakdown point of all three estimators is 50%. However, Sₙ and Qₙ are much more efficient than\ MADₙ: their asymptotic Gaussian efficiency values are 58% and 82% respectively compared to 37% for\ MADₙ. Although these values look impressive, they are only asymptotic values. The actual Gaussian efficiency of Sₙ and Qₙ for small sample sizes is noticeable lower than in the asymptotic case. The original work by Rousseeuw and Croux (1993) provides only rough approximations of the finite-sample bias-correction factors for Sₙ, Qₙ and brief notes on their finite-sample efficiency values. In this paper, we perform extensive Monte-Carlo simulations in order to obtain refined values of the finite-sample properties of the Rousseeuw-Croux scale estimators. We present accurate values of the bias-correction factors and Gaussian efficiency for small samples (n ≤100) and prediction equations for samples of larger sizes.
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