{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "9D47D1Q89E"
    },
    {
      "field": "about",
      "target": "FB692YN0BZ"
    },
    {
      "field": "uses",
      "target": "FB692YN0BZ"
    }
  ],
  "body": "\n## Summary\n\nA minimax estimator is an estimator whose worst-case [[risk|N26TSVRH2S]], over all values of the unknown parameter, is as small as possible.\nThe smallest achievable worst-case risk is the minimax risk of the problem.\nThe minimax principle gives a way to choose among estimators without a prior, and it is a basic benchmark in decision theory and nonparametric statistics.\n\n## Explanations\n\n### L1 human\n\nImagine that an opponent picks the true parameter after seeing which estimator is used, so as to make it look as bad as possible.\nA minimax estimator is the best choice against such an opponent.\nIt may be a little worse than others for typical parameters, but it guards against the worst case.\nFor a coin tossed $n$ times, the minimax estimator of the heads probability under squared error is $(X + \\sqrt{n}/2)/(n + \\sqrt{n})$, not the plain proportion $X/n$.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "62C20"
    ],
    "name": "Minimax estimator",
    "same_as": {
      "wikidata": "Q6865379",
      "wikipedia": "Minimax estimator"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Minimax_estimator"
      }
    ],
    "tag": "8EG1M1WZ9C"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/8EG1M1WZ9C/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/8EG1M1WZ9C.md",
  "msc": [
    "62C20"
  ],
  "name": "Minimax estimator",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/8EG/8EG1M1WZ9C.md",
  "status": null,
  "tag": "8EG1M1WZ9C",
  "uri": "m2://8EG1M1WZ9C",
  "url": "https://tamnd.github.io/math2/wiki/minimax-estimator/",
  "writing": {
    "tag": "8EG1M1WZ9C",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}