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  "body": "\n## Summary\n\nAn M-estimator is an estimator defined as the minimizer of a sum of a loss function over the observations.\nLeast squares, least absolute deviations and maximum likelihood are all M-estimators.\nThe class was introduced in robust statistics, where the loss is chosen to limit the influence of outliers.\nA single general theory gives consistency and asymptotic normality for the whole class.\n\n## Explanations\n\n### L1 human\n\nChoose a way to measure how badly a candidate value $\\theta$ fits one observation, for example the squared distance $(x - \\theta)^2$.\nAdd up these penalties over all observations and take the $\\theta$ with the smallest total.\nWith squared distance you get the sample mean; with absolute distance $\\abs{x - \\theta}$ you get the sample median.\nOther penalties, which grow more slowly for far-away points, give estimates that are less disturbed by outliers.\n",
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