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  "body": "\n## Summary\n\nThe James–Stein estimator estimates the mean vector of a multivariate normal distribution in dimension $p \\ge 3$ by shrinking the observation toward a fixed point.\nUnder squared error loss its risk is strictly smaller than that of the observation itself, for every value of the mean.\nIt is the standard illustration of [[Stein's example|7SC9E65XDN]] and the prototype of [[shrinkage estimators|GPBSS1V3SS]].\n\n## Explanations\n\n### L1 human\n\nSuppose one observes a noisy vector $X$ whose average is the unknown vector $\\theta$.\nThe James–Stein estimator multiplies $X$ by a factor a bit smaller than $1$, pulling it toward the origin.\nThe factor is close to $1$ when $X$ is far from the origin, and smaller when $X$ is close to it.\nFor example, with $p = 3$, unit noise and observation $X = (1, 1, 1)$, the factor is $1 - 1/3$, and the estimate is $(2/3, 2/3, 2/3)$.\n",
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