Robustness
Overview
Published Online: Jan 28 2011
DOI: 10.1002/wics.144
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Abstract That the conclusion based on a data analysis be robust and stable is not merely a desirable feature, it is essential. To merit this quality label, a conclusion must be supported by strong data‐based evidence and not simply be a discovery gleaned from a preconceived model and weakly supported by a part of the data. Robustness in statistics refers to the definition and investigation of procedures that lead to such stability. This article gives a brief overview of the concepts and procedures that are relevant in judging robustness. These have mostly been developed over the last five decades. WIREs Comp Stat 2011 3 85–94 DOI: 10.1002/wics.144 This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Statistical and Graphical Methods of Data Analysis > Robust Methods
The plot shows how M‐estimators work. The three curves correspond to ψ(x − T), for the mean, the median, and the Huber estimator with k = 1.5. The sample values are X1 = −1, X2 = 0, X3 = 4. The vertical grey lines indicate the positions of the observations. The estimators are Tn = 1 for the mean, Tn = 0.25 for the Huber estimator, and Tn = 0 for the median. These values are such that the sum of ψ(Xi − Tn) is equal to zero. Note how these values are ordered from most robust to least robust. The outlier at 4 pulls the mean toward the right, while the median resists and stays at zero. The Huber estimator is in between.
