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  "body": "\n## Summary\n\nEmpirical likelihood is a method of inference that uses a [[likelihood|0VW9E4QXR6]] ratio without assuming a parametric family.\nIt assigns unknown weights to the observed data points and maximises the product of the weights under a constraint given by the parameter value.\nIt then compares the result with the unconstrained maximum.\nArt Owen developed it in the late 1980s.\nLike a parametric likelihood ratio, it yields tests and confidence regions with chi-squared calibration, and its confidence regions take their shape from the data.\n\n## Explanations\n\n### L1 human\n\nA parametric likelihood asks how probable the data are under a formula for the distribution.\nEmpirical likelihood avoids the formula: it only allows distributions that put weight on the observed points.\nTo judge a proposed mean $\\mu$, it tilts the weights as little as possible so that the weighted average of the data equals $\\mu$.\nThe more the weights must be tilted, the less plausible $\\mu$ is.\nIf $\\mu$ is the sample mean, no tilting is needed and the ratio is $1$.\n",
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