# 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

Abstract:

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

@article{akinshin2022frc,
title = {Finite-sample Rousseeuw-Croux scale estimators},
author = {Akinshin, Andrey},
year = {2022},
month = {9},
publisher = {arXiv},
doi = {10.48550/arXiv.2209.12268},
url = {https://arxiv.org/abs/2209.12268}
}


The source code of this post and all the relevant files are available on GitHub.
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