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  "body": "\n## Summary\n\nKernel density estimation estimates an unknown [[probability density|0ZY9DX8FBF]] from a sample by placing a small bump, the kernel, at each observation and averaging the bumps.\nThe width of the bumps, the bandwidth, controls the trade-off between bias and variance.\nIt is a basic method of [[nonparametric statistics|VFAJ1EG3X5]] and a smooth alternative to the histogram.\n\n## Explanations\n\n### L1 human\n\nPut a small hill of total area $1/n$ on top of each of the $n$ data points and add the hills.\nThe result is a smooth curve of total area $1$ that is high where the data are dense.\nNarrow hills give a wiggly curve that follows every point; wide hills give a smooth curve that may hide real features.\nWith the Gaussian bump, the estimate is an average of $n$ normal densities centred at the data points.\n",
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