Finite-sample Rousseeuw-Croux scale estimators
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The Rousseeuw-Croux S_n, Q_n scale estimators and the median absolute deviation MAD_n 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, S_n and Q_n are much more efficient than MAD_n: their asymptotic Gaussian efficiency values are 58% and 82% respectively compared to 37% forMAD_n. Although these values look impressive, they are only asymptotic values. The actual Gaussian efficiency of S_n and Q_n 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 S_n, Q_n 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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