{
  "$schema": "../../../schemas/mko-v0.4.schema.json",
  "schema_version": "mko-v0.4",
  "id": "mko-statistical-estimator",
  "semantic_family_id": "sf-statistical-estimator",
  "type": "definition",
  "version": "0.10.0",
  "language": "zh-Hant",
  "titles": {
    "zh-Hant": "統計估計量"
  },
  "summary": {
    "zh-Hant": "估計量是固定且不依未知theta的可測total statistic；觀察後數值是estimate。"
  },
  "statement": {
    "zh-Hant": "有限parameter model與共同sample space上，statistic table只依observation。逐theta可計算expectation但本輪不宣稱unbiased、consistent、sufficient、identifiable或posterior；完整sampling distribution留後續節點。"
  },
  "formula": {
    "tex": "E(X)",
    "mathml": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>E</mi><mo>(</mo><mi>X</mi><mo>)</mo></mrow></math>",
    "semantic_ast": {
      "type": "function_call",
      "callee": {
        "type": "symbol",
        "name": "E",
        "glyph": "E"
      },
      "arguments": [
        {
          "type": "symbol",
          "name": "X",
          "glyph": "X"
        }
      ]
    },
    "compiler": {
      "id": "ocme-formula-core",
      "version": "0.4.0",
      "source_sha256": "f5418721593e95478e11dfda98de2ce40bff03e6c81cba28b8e64da36ae9926d"
    }
  },
  "assumptions": [
    {
      "id": "a1",
      "zh-Hant": "共同有限sample space與已驗parametric model。"
    },
    {
      "id": "a2",
      "zh-Hant": "statistic對每個outcome恰有一個值且不以theta索引。"
    }
  ],
  "symbols": [
    {
      "token": "E",
      "role": "statistical_estimator",
      "role_zh": "估計量",
      "scope": "representative_formula"
    },
    {
      "token": "X",
      "role": "sample_observation",
      "role_zh": "樣本觀察",
      "scope": "representative_formula"
    }
  ],
  "dependencies": [
    {
      "id": "mko-parametric-statistical-model",
      "title_zh": "參數統計模型",
      "reason_zh": "逐theta laws。"
    },
    {
      "id": "mko-random-variable",
      "title_zh": "隨機變數",
      "reason_zh": "statistic為樣本函數。"
    },
    {
      "id": "mko-sample-space",
      "title_zh": "樣本空間",
      "reason_zh": "total domain。"
    }
  ],
  "explanation": {
    "paragraphs_zh": [
      "estimator是函數，estimate是觀察值。",
      "函數不可依未知theta。",
      "properties與sampling law另證。"
    ],
    "common_misconception_zh": "把estimate當estimator，或把theta塞入statistic定義。"
  },
  "proofs": [],
  "computational_companions": [],
  "verification": {
    "computational_status": "not_evaluated_no_computational_claim",
    "warning_zh": "只核有限total statistic及逐theta expectation，不推統計性質。",
    "evidence_refs": [],
    "producers": [
      {
        "id": "lean-mathlib",
        "adapter": "formal_system",
        "config_path": "formal/lean/lakefile.toml",
        "status": "configured"
      }
    ]
  },
  "formalization": {
    "status": "not_formalized",
    "target_systems": [
      "Lean 4",
      "Mathlib"
    ],
    "next_obligation_zh": "加入sampling distribution、bias與variance。"
  },
  "provenance": {
    "origin": "ocme_local_ai_materialization_candidate",
    "note_zh": "依 research/atlas-statistical-estimator.md 整理；2026-10-14 脈衝 R04（使用者手動接續 2026-11-04 工作序列；實際日期仍為 2026-10-14），英文及 Lean 依使用者指示延後。",
    "content_license": "CC-BY-SA-4.0",
    "code_license": "MIT",
    "created_at": "2026-10-14"
  }
}