Robust statistics represent an alternative approach to parameter estimation, differing from nonrobust statistics (sometimes called classical statistics) in the degree to which they are affected by violations of model assumptions. Whereas nonrobust statistics are greatly affected by small violations of their underlying assumptions, robust statistics are only slightly affected by such violations. Statisticians have focused primarily on designing statistics that are robust to violations of normality, due to both the frequency of nonnormality (e.g., via outliers) and its unwanted impact on commonly used statistics that assume normality (e.g., standard error of the mean). Nevertheless, robust statistics also exist that minimize the impact of violations other than nonnormality (e.g., heteroscedasticity).

Figure 1 A Normal Distributiona (black line), and a Mixed Normal Distributionb (dashed line)

Source: Adapted from Wilcox ...

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