2022/09/25 by Andrey Akinshin, Akinshin, Andrey
Decision Sciences · Mathematics · #62G05 #62G35 #62Q05 #FOS: Computer and information sciences #Forecasting Techniques and Applications #Methodology (stat.ME) #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.2209.12268
openalex publication_date 2022/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.