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  "body": "\n## Definition\n\nLet $\\Theta$ be a set of parameters, and for each $\\theta \\in \\Theta$ let $P_\\theta$ be a probability distribution. Let $X_1, \\dots, X_n$ be a sample whose joint law is determined by an unknown $\\theta \\in \\Theta$. Let $\\tau \\colon \\Theta \\to \\mathbb{R}^k$ be a function.\nAn estimator of $\\tau(\\theta)$ is a [[statistic|036756NFD6]] $\\hat{\\tau} = g(X_1, \\dots, X_n)$ with values in $\\mathbb{R}^k$, where $g$ does not depend on $\\theta$.\nThe value of $\\hat{\\tau}$ for observed data is an estimate of $\\tau(\\theta)$.\n\n## Remarks\n\nThe definition does not ask that $\\hat{\\tau}$ is close to $\\tau(\\theta)$. One measures the quality of an estimator with its [[bias|01BD2TFFP4]], its variance and its [[mean squared error|0V4VSCBXP3]].\nFor an i.i.d. sample, the sample mean is an estimator of the mean, and the sample variance is an estimator of the variance.\nOne often writes $\\hat{\\theta}$ for an estimator of $\\theta$ itself.\n\n## Explanations\n\n### L1 human\n\nAn estimator is a recipe that turns data into a guess of an unknown quantity.\nFor example, the fraction of \"yes\" answers in a poll is an estimator of the fraction of \"yes\" voters in the whole population.\n",
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