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  "body": "\n## Summary\n\nA U-statistic is the average of a symmetric function, the kernel, over all subsets of a fixed size of the observations.\nIt is an unbiased estimator of the mean of the kernel.\nThe sample mean, the sample variance, Kendall's $\\tau$ and the Mann–Whitney statistic are U-statistics or close relatives of them.\nUnder mild conditions, Hoeffding's theory gives their asymptotic normality in one stroke.\n\n## Explanations\n\n### L1 human\n\nSuppose you want to estimate the average squared distance between two random members of a population.\nTake every pair of points in your sample, compute half their squared distance, and average over all pairs.\nThis average is a U-statistic, and it turns out to be exactly the usual sample variance.\nAveraging over all subsets, instead of using only some of them, uses the data as fully as possible.\n",
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