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  "body": "\n## Summary\n\nThe influence function of a statistical functional measures the effect on the functional of adding an infinitesimal amount of contamination at a point $x$.\nIt is a directional derivative of the functional in the direction of a point mass, a [[Gateaux derivative|EAZF9NJW12]].\nA bounded influence function means that no single observation can have a large effect, and the supremum of its absolute value is the gross-error sensitivity.\nUnder regularity conditions it also gives the asymptotic variance of the estimator, so it links robustness and efficiency.\n\n## Explanations\n\n### L1 human\n\nImagine a huge data set, and add one more point at position $x$.\nThe estimate moves a little; the influence function records how much, per unit of added weight, as a function of $x$.\nFor the mean, the effect grows without limit as $x$ moves away, so a far outlier has a large effect.\nFor the median, the effect is the same for every point above the median, however far away, so outliers have limited effect.\n",
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        "what": "an inventory row",
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