Alternatives to the Median Absolute Deviation

By Peter J. Rousseeuw, Christophe Croux. 1993

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Citations in the corpus

Neural Cleanse: Identifying and Mitigating Backdoor Attacks in Neural Networks (2019, background): “MAD was first presented on symmetric distribution, but later work show that it also work on asymmetric distribution [21].”
Robust and efficient estimation of the mode of continuous data: the mode as a viable measure of central tendency (2003, background): “The MAD is preferred for these studies with large numbers of outliers since its asymptotic breakdown point is twice that of the interquartile range (Rousseeuw and Croux, 1993).”
Comparing variances and other measures of dispersion (2004, background): “…face of extremely large outliers, say generated from the Cauchy distribution, one might want to consider more robust scale estimators such as those based on trimmed averages of the |Xij − Xik| (e.g., GLG of Boos and Brownie, 1989, page 73) or single ordered values (Qn of Rousseeuw and Croux, 1993).”
Variations of Q–Q Plots: The Power of Our Eyes! (2015, methodology): “We could use alternative estimators for variance, such as median absolute deviation (MAD) or adjusted MAD (Rousseeuw and Croux, 1993), but this will likely also change the power of the corresponding lineup.”
A robust approach for estimating change-points in the mean of an AR(1) process (2014, background): “ρ̂MG = Q 2 n(y +) − Q2n(y−) Q(2)n(y +) + Q2n(y−) , where y+ = (yi+1 + yi)0≤i≤n−1, y− = (yi+1 − yi)0≤i≤n−1 and Qn is the scale estimator of [33] which is such that Qn(x) is proportional to the first quartile of {|xi − xj |;0 ≤ i < j ≤ n}.”
Estimation of Power System Inertia From Ambient Wide Area Measurements (2018, background): “, n}, xi are the values in that sample, and c is a term introduced to achieve consistency with the standard deviation of a certain distribution [31].”
Robust High-Dimensional Precision Matrix Estimation (2014, background): “,x) ∈ Rn×p, where scale() is a robust scale estimate like the median absolute deviation or the Qn-estimator [Rousseeuw and Croux, 1993].”
The dual-bootstrap iterative closest point algorithm with application to retinal image registration (2003, background): “Initialization can be addressed in a variety of ways, including image-wide measurements [36], [40], multiresolution [5], [27], [66], [67], indexing and initial matching of distinctive features or sets of features [18], [21], [44], [69], [75], and minimal-subset (of possible correspondences) random-s”
Robust machine learning by median-of-means: Theory and practice (2017, background): “Other generalization to quantile estimation can be found in [78].”
Applying Robust Methods to Operational Risk Modeling (2006, background): “Robust measures of spread include inter-quartile range (IQR), median absolute deviation (MAD), mean absolute deviation, and Winsorized standard deviation; more estimators of scale were proposed by Rousseeuw and Croux (1993).”
Outlyingness weighted covariation (2011, unknown): “(5)The univariate counterpart of the MCD covariance estimator is the least trimmed squares scale estimator, but many other jump robust variance estimators that are consistent at the normal distribution can be used, such as the median absolute deviation or the Qn estimator (Rousseeuw and Croux, 1993)”