Finite-sample bias correction factors for Rousseeuw-Croux scale estimators

The Rousseeuw-Croux scale estimators \(S_n\) and \(Q_n\) are efficient alternatives to the median absolute deviation (\(\operatorname{MAD}_n\)). While all three estimators have the same breakdown point of \(50\%\), \(S_n\) and \(Q_n\) have higher statistical efficiency than \(\operatorname{MAD}_n\). The asymptotic Gaussian efficiency values of \(\operatorname{MAD}_n\), \(S_n\), and \(Q_n\) are \(37\%\), \(58\%\), and \(82\%\) respectively. Using scale constants, we can make \(S_n\) and \(Q_n\) c...

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