Preprint announcement: 'Finite-sample Rousseeuw-Croux scale estimators'

Recently, I published a preprint of a paper ‘Finite-sample Rousseeuw-Croux scale estimators’. It’s based on a series of my research notes.

The paper preprint is available on arXiv: arXiv:2209.12268 [stat.ME]. The paper source code is available on GitHub: AndreyAkinshin/paper-frc. You can cite it as follows:

  • Andrey Akinshin (2022) “Finite-sample Rousseeuw-Croux scale estimators” arXiv:2209.12268


The Rousseeuw-Croux \(S_n\), \(Q_n\) scale estimators and the median absolute deviation \(\operatorname{MAD}_n\) 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 \(\operatorname{MAD}_n\): their asymptotic Gaussian efficiency values are \(58\%\) and \(82\%\) respectively compared to \(37\%\) for \(\operatorname{MAD}_n\). 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 noticeably 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 (\(n \leq 100\)) and prediction equations for samples of larger sizes.

Relevant blog posts

Here is the full list of the relevant blog posts:

BibTeX reference

  title = {Finite-sample Rousseeuw-Croux scale estimators},
  author = {Akinshin, Andrey},
  year = {2022},
  month = {9},
  publisher = {arXiv},
  doi = {10.48550/arXiv.2209.12268},
  url = {}