{"id":257,"date":"2023-08-03T13:00:58","date_gmt":"2023-08-03T13:00:58","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e4%bc%b0%e8%ae%a1%e5%99%a8\/"},"modified":"2023-08-03T13:00:58","modified_gmt":"2023-08-03T13:00:58","slug":"%e4%bc%b0%e8%ae%a1%e5%99%a8","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e4%bc%b0%e8%ae%a1%e5%99%a8\/","title":{"rendered":"\u4f30\u7b97\u5668"},"content":{"rendered":"

\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u4f30\u8ba1\u5668\u662f\u4ec0\u4e48\u4ee5\u53ca\u597d\u7684\u4f30\u8ba1\u5668\u5177\u6709\u54ea\u4e9b\u5c5e\u6027\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u4f30\u8ba1\u5668\u7684\u793a\u4f8b\u4ee5\u53ca\u7edf\u8ba1\u4e2d\u5b58\u5728\u7684\u4e0d\u540c\u7c7b\u578b\u7684\u4f30\u8ba1\u3002<\/p>\n

<\/span>\u4ec0\u4e48\u662f\u4f30\u7b97\u5668\uff1f<\/span><\/h2>\n

\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u4f30\u8ba1\u91cf<\/strong>\u662f\u7528\u4e8e\u4f30\u8ba1\u603b\u4f53\u53c2\u6570\u503c\u7684\u7edf\u8ba1\u91cf\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u4f30\u8ba1\u5668\u7528\u4e8e\u4f30\u8ba1\u603b\u4f53\u7684\u672a\u77e5\u53c2\u6570\u3002<\/p>\n

\u4f8b\u5982\uff0c\u6837\u672c\u5e73\u5747\u503c\u662f\u603b\u4f53\u5e73\u5747\u503c\u7684\u4f30\u8ba1\u91cf\u3002\u56e0\u6b64\uff0c\u60a8\u53ef\u4ee5\u8ba1\u7b97\u6837\u672c\u7684\u7b97\u672f\u5e73\u5747\u503c\uff0c\u5e76\u5c06\u8be5\u503c\u7528\u4f5c\u603b\u4f53\u5e73\u5747\u503c\u7684\u8fd1\u4f3c\u503c\u3002<\/p>\n

\u62bd\u6837\u4f30\u8ba1\u91cf\u5728\u7edf\u8ba1\u5b66\u4e2d\u975e\u5e38\u5e38\u89c1\uff0c\u56e0\u4e3a\u901a\u5e38\u5e76\u975e\u603b\u4f53\u7684\u6240\u6709\u5143\u7d20\u90fd\u662f\u5df2\u77e5\u7684\uff0c\u56e0\u6b64\u65e0\u6cd5\u8ba1\u7b97\u603b\u4f53\u7684\u7edf\u8ba1\u53c2\u6570\u3002\u63a5\u4e0b\u6765\uff0c\u9009\u62e9\u968f\u673a\u6837\u672c\u5e76\u786e\u5b9a\u6837\u672c\u7684\u7edf\u8ba1\u5ea6\u91cf\uff0c\u7136\u540e\u6839\u636e\u6240\u505a\u7684\u8ba1\u7b97\uff0c\u53ef\u4ee5\u8fd1\u4f3c\u4f30\u8ba1\u603b\u4f53\u53c2\u6570\u3002 <\/p>\n

<\/span>\u4f18\u79c0\u4f30\u7b97\u5668\u7684\u7279\u5f81<\/span><\/h2>\n

\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u4f30\u8ba1\u5668\u7684\u5b9a\u4e49\uff0c\u8ba9\u6211\u4eec\u770b\u770b\u4e00\u4e2a\u597d\u7684\u4f30\u8ba1\u5668\u5fc5\u987b\u5177\u5907\u54ea\u4e9b\u7279\u5f81\u624d\u80fd\u66f4\u597d\u5730\u7406\u89e3\u8fd9\u4e2a\u6982\u5ff5\u3002<\/p>\n

    \n
  1. \u65e0\u504f<\/strong>\uff1a\u65e0\u504f\u4f30\u8ba1\u91cf\u662f\u6837\u672c\u503c\u7b49\u4e8e\u603b\u4f53\u503c\u7684\u4f30\u8ba1\u91cf\u3002\u56e0\u6b64\uff0c\u4f30\u8ba1\u91cf\u7684\u504f\u5dee\u8d8a\u5927\uff0c\u5176\u7cbe\u786e\u5ea6\u5c31\u8d8a\u4f4e\u3002\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u6211\u4eec\u5e0c\u671b\u70b9\u4f30\u8ba1\u5668\u7684\u504f\u5dee\u5f88\u5c0f\uff0c\u4f7f\u5f97\u70b9\u4f30\u8ba1\u5668\u503c\u4e0e\u771f\u5b9e\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u5c3d\u53ef\u80fd\u63a5\u8fd1\u4e8e\u96f6\u3002<\/span><\/li>\n
  2. \u4e00\u81f4\u6027<\/strong>\uff1a\u4e00\u81f4\u6027\u4f30\u8ba1\u91cf\u662f\u6307\u968f\u7740\u6837\u672c\u91cf\u7684\u589e\u52a0\uff0c\u5176\u503c\u63a5\u8fd1\u53c2\u6570\u7684\u771f\u5b9e\u503c\u7684\u4f30\u8ba1\u91cf\u3002\u56e0\u6b64\uff0c\u6837\u672c\u91cf\u8d8a\u5927\uff0c\u4ea7\u751f\u7684\u4f30\u8ba1\u5c31\u8d8a\u597d\u3002<\/span><\/li>\n
  3. \u6548\u7387<\/strong>\uff1a\u70b9\u4f30\u8ba1\u5668\u7684\u91c7\u6837\u5206\u5e03\u7684\u65b9\u5dee\u8d8a\u5c0f\uff0c\u70b9\u4f30\u8ba1\u5668\u7684\u6548\u7387\u5c31\u8d8a\u5927\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5e0c\u671b\u70b9\u4f30\u8ba1\u5668\u9ad8\u6548\uff0c\u4ee5\u4fbf\u65b9\u5dee\u5f88\u5c0f\u3002\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u4ec5\u4ec5\u4f9d\u9760\u8fd9\u4e2a\u7279\u6027\uff0c\u5728\u4e24\u4e2a\u70b9\u4f30\u8ba1\u5668\u4e4b\u95f4\u6211\u4eec\u5c06\u59cb\u7ec8\u9009\u62e9\u6548\u7387\u6700\u9ad8\uff08\u6216\u65b9\u5dee\u6700\u4f4e\uff09\u7684\u4f30\u8ba1\u5668\u3002<\/span><\/li>\n
  4. \u9c81\u68d2\u6027<\/strong>\uff1a\u9c81\u68d2\u4f30\u8ba1\u91cf\u662f\u6307\u5728\u4fee\u6539\u67d0\u4e9b\u521d\u59cb\u5047\u8bbe\u7684\u60c5\u51b5\u4e0b\uff0c\u4f30\u8ba1\u7ed3\u679c\u4e0d\u4f1a\u53d1\u751f\u91cd\u5927\u4fee\u6539\u7684\u4f30\u8ba1\u91cf\u3002<\/span><\/li>\n
  5. \u5145\u5206\u6027<\/strong>\uff1a\u5982\u679c\u4e00\u4e2a\u4f30\u8ba1\u5668\u603b\u7ed3\u4e86\u4f30\u8ba1\u4e2d\u6709\u5173\u6837\u672c\u7684\u6240\u6709\u76f8\u5173\u4fe1\u606f\uff0c\u5219\u8be5\u4f30\u8ba1\u5668\u5c31\u8db3\u591f\u4e86\uff0c\u8fd9\u6837\u5c31\u6ca1\u6709\u5176\u4ed6\u4f30\u8ba1\u5668\u53ef\u4ee5\u63d0\u4f9b\u6709\u5173\u4f30\u8ba1\u603b\u4f53\u53c2\u6570\u7684\u9644\u52a0\u4fe1\u606f\u3002\u56e0\u6b64\uff0c\u5f53\u53ef\u4ee5\u9009\u62e9\u8fd1\u4f3c\u603b\u4f53\u53c2\u6570\u7684\u6700\u4f73\u7edf\u8ba1\u91cf\u65f6\uff0c\u4e00\u4e2a\u4f30\u8ba1\u91cf\u5c31\u8db3\u591f\u4e86\u3002<\/span> <\/li>\n<\/ol>\n

    <\/span>\u4f30\u8ba1\u5668\u7684\u4f8b\u5b50<\/span><\/h2>\n

    \u901a\u5e38\uff0c\u4ee5\u4e0b\u6837\u672c\u4f30\u8ba1\u91cf\u88ab\u7528\u4f5c\u603b\u4f53\u53c2\u6570\u7684\u4f30\u8ba1\u3002<\/p>\n

      \n
    • \u603b\u4f53\u5e73\u5747\u503c\u7684\u70b9\u4f30\u8ba1\u662f\u6837\u672c\u7684\u7b97\u672f\u5e73\u5747\u503c\u3002\u4e00\u822c\u60c5\u51b5\u4e0b\uff0c\u4f7f\u7528\u7b26\u53f7\n

      \"\\overline{x}\"<\/p>\n

      <\/span>\u8868\u793a\u6837\u672c\u5747\u503c\u7684\u503c\uff0c\u800c\u603b\u4f53\u5747\u503c\u7684\u7b26\u53f7\u662f\u5e0c\u814a\u5b57\u6bcd\u03bc\u3002 <\/li>\n<\/ul>\n

      \"\\overline{x}=\\mu\"<\/p>\n<\/p>\n

        \n
      • \u901a\u8fc7\u6837\u672c\u6807\u51c6\u5dee\u503c\u53ef\u4ee5\u51c6\u786e\u4f30\u8ba1\u603b\u4f53\u7684\u6807\u51c6\u5dee\uff08\u6216\u6807\u51c6\u5dee\uff09\u3002\u603b\u4f53\u6807\u51c6\u5dee\u7528\u5e0c\u814a\u5b57\u6bcd\u03c3\u8868\u793a\uff0c\u6837\u672c\u6807\u51c6\u5dee\u503c\u7528\u5b57\u6bcds\u8868\u793a\u3002<\/span> <\/li>\n<\/ul>\n

        \"s=\\sigma\"<\/p>\n<\/p>\n

          \n
        • \u53ef\u4ee5\u901a\u8fc7\u6837\u672c\u6bd4\u4f8b\u503c\u4ee5\u7279\u5b9a\u65b9\u5f0f\u4f30\u8ba1\u603b\u4f53\u6bd4\u4f8b\u3002\u603b\u4f53\u6bd4\u4f8b\u7684\u7b26\u53f7\u662f\u5b57\u6bcd py\uff0c\u6837\u672c\u6bd4\u4f8b\u7684\u7b26\u53f7\u662f\n

          \"\\widehat{p}.\"<\/p>\n

          <\/span><\/li>\n<\/ul>\n

          \"\\widehat{p}=p\"<\/p>\n<\/p>\n

          <\/span>\u4f30\u8ba1\u5668\u548c\u4f30\u8ba1<\/span><\/h2>\n

          \u6b63\u5982\u6574\u7bc7\u6587\u7ae0\u6240\u89e3\u91ca\u7684\uff0c\u4f30\u8ba1\u5668\u7528\u4e8e\u4f30\u8ba1\u603b\u4f53\u53c2\u6570\u3002\u4f46\u662f\uff0c\u5e94\u8be5\u8bb0\u4f4f\uff0c\u6709\u4e24\u79cd\u7c7b\u578b\u7684\u4f30\u8ba1\uff1a<\/p>\n

            \n
          • \u70b9\u4f30\u8ba1<\/strong>\uff1a\u5305\u62ec\u5c06\u53c2\u6570\u7684\u6837\u672c\u503c\u4f5c\u4e3a\u603b\u4f53\u503c\u7684\u8fd1\u4f3c\u503c\u3002<\/span><\/li>\n
          • \u533a\u95f4\u4f30\u8ba1<\/strong>\uff1a\u6d89\u53ca\u5728\u4e00\u5b9a\u533a\u95f4\u5185\u8fd1\u4f3c\u603b\u4f53\u53c2\u6570\u7684\u503c\uff0c\u800c\u4e0d\u662f\u7279\u5b9a\u503c\u3002\u56e0\u6b64\uff0c\u5728\u8fd9\u79cd\u7c7b\u578b\u7684\u4f30\u8ba1\u4e2d\uff0c\u8ba1\u7b97\u51fa\u4e00\u4e2a\u533a\u95f4\uff0c\u5176\u4e2d\u53c2\u6570\u7684\u771f\u5b9e\u503c\u4f4d\u4e8e\u8be5\u533a\u95f4\u5185\u7684\u6982\u7387\u975e\u5e38\u9ad8\u3002<\/span><\/li>\n<\/ul>\n

            \u6bcf\u79cd\u7c7b\u578b\u7684\u4f30\u8ba1\u90fd\u6709\u5176\u4f18\u70b9\u548c\u7f3a\u70b9\uff0c\u6839\u636e\u5177\u4f53\u60c5\u51b5\uff0c\u4f7f\u7528\u70b9\u4f30\u8ba1\u6216\u533a\u95f4\u4f30\u8ba1\u66f4\u4e3a\u5b9e\u7528\u3002\u5982\u9700\u4e86\u89e3\u66f4\u591a\u4fe1\u606f\uff0c\u60a8\u53ef\u4ee5\u5728\u672c\u7ad9\u641c\u7d22\u5f15\u64ce\u4e2d\u641c\u7d22\u6211\u4eec\u76f8\u5e94\u7684\u6587\u7ae0\u3002<\/p>\n

            <\/span>\u4f30\u8ba1\u5668\u7684\u8bef\u5dee<\/span><\/h2>\n

            \u5728\u5b9e\u8df5\u4e2d\uff0c\u8981\u51c6\u786e\u4f30\u8ba1\u53c2\u6570\u7684\u771f\u5b9e\u503c\u662f\u975e\u5e38\u56f0\u96be\u7684\uff0c\u8fd9\u5c31\u662f\u4f30\u8ba1\u7ecf\u5e38\u51fa\u73b0\u8bef\u5dee\u7684\u539f\u56e0\u3002\u4ece\u903b\u8f91\u4e0a\u8bb2\uff0c\u6211\u4eec\u5fc5\u987b\u5c3d\u91cf\u51cf\u5c11\u4f30\u8ba1\u8bef\u5dee\u3002<\/p>\n

            \u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u4f30\u8ba1\u5668\u7684\u8bef\u5dee\u5b9a\u4e49\u4e3a\u53c2\u6570\u7684\u4f30\u8ba1\u503c\u4e0e\u771f\u5b9e\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u3002<\/p>\n<\/p>\n

            \"e=\\widehat{\\theta}-\\theta\"<\/p>\n<\/p>\n

            \u91d1\u5b50<\/p>\n<\/p>\n

            \"\\widehat{\\theta}\"<\/p>\n

            \u662f\u4f30\u8ba1\u503c\uff0c<\/p>\n

            \"\\theta\"<\/p>\n

            \u662f\u53c2\u6570\u7684\u5b9e\u9645\u503c\u3002<\/p>\n

            \u60a8\u8fd8\u53ef\u4ee5\u8ba1\u7b97\u5747\u65b9\u8bef\u5dee (MSE)\uff0c\u5373\u5e73\u65b9\u8bef\u5dee\u7684\u5e73\u5747\u503c\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5747\u65b9\u8bef\u5dee\u4ee3\u8868\u4e86\u4f30\u8ba1\u91cf\u7684\u65b9\u5dee\u3002<\/p>\n<\/p>\n

            \"\\displaystyle<\/p><\/p>\n","protected":false},"excerpt":{"rendered":"

            \u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u4f30\u8ba1\u5668\u662f\u4ec0\u4e48\u4ee5\u53ca\u597d\u7684\u4f30\u8ba1\u5668\u5177\u6709\u54ea\u4e9b\u5c5e\u6027\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u4f30\u8ba1\u5668\u7684\u793a\u4f8b\u4ee5\u53ca\u7edf\u8ba1\u4e2d\u5b58\u5728\u7684\u4e0d\u540c […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-257","post","type-post","status-publish","format-standard","hentry","category-14"],"yoast_head":"\n\u25b7 \u4ec0\u4e48\u662f\u4f30\u7b97\u5668\uff1f \uff08\u7edf\u8ba1\u6570\u636e\uff09<\/title>\n<meta name=\"description\" content=\"\u5728\u8fd9\u91cc\uff0c\u60a8\u5c06\u4e86\u89e3\u7edf\u8ba1\u5b66\u4e2d\u7684\u4f30\u8ba1\u5668\u662f\u4ec0\u4e48\u3001\u4f18\u79c0\u4f30\u8ba1\u5668\u7684\u7279\u5f81\u4ee5\u53ca\u4f30\u8ba1\u5668\u7684\u793a\u4f8b\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/cn\/\u4f30\u8ba1\u5668\/\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 \u4ec0\u4e48\u662f\u4f30\u7b97\u5668\uff1f \uff08\u7edf\u8ba1\u6570\u636e\uff09\" \/>\n<meta property=\"og:description\" content=\"\u5728\u8fd9\u91cc\uff0c\u60a8\u5c06\u4e86\u89e3\u7edf\u8ba1\u5b66\u4e2d\u7684\u4f30\u8ba1\u5668\u662f\u4ec0\u4e48\u3001\u4f18\u79c0\u4f30\u8ba1\u5668\u7684\u7279\u5f81\u4ee5\u53ca\u4f30\u8ba1\u5668\u7684\u793a\u4f8b\u3002\" \/>\n<meta property=\"og:url\" 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