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Robustness

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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(xT), 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(XiTn) 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.

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Statistical and Graphical Methods of Data Analysis > Nonparametric Methods
Statistical and Graphical Methods of Data Analysis > Robust Methods
Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis

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