{"id":29363,"date":"2021-10-20T19:37:20","date_gmt":"2021-10-20T11:37:20","guid":{"rendered":"https:\/\/swarma.org\/?p=29363"},"modified":"2021-10-20T19:37:20","modified_gmt":"2021-10-20T11:37:20","slug":"donald-rubin%e7%9a%84%e5%9b%a0%e6%9e%9c%e6%8e%a8%e6%96%ad%e5%ad%a6%e6%9c%af%e8%b4%a1%e7%8c%ae%ef%bc%9a%e8%b6%85%e5%87%ba%e7%bb%9f%e8%ae%a1%e5%ad%a6%e8%8c%83%e7%95%b4%e7%9a%84%e5%88%92%e6%97%b6","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=29363","title":{"rendered":"Donald Rubin\u7684\u56e0\u679c\u63a8\u65ad\u5b66\u672f\u8d21\u732e\uff1a\u8d85\u51fa\u7edf\u8ba1\u5b66\u8303\u7574\u7684\u5212\u65f6\u4ee3\u5f71\u54cd"},"content":{"rendered":"
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<\/strong>2021\u5e7410\u670811\u65e5\uff0cJoshua D. Angrist\u548cGuido W. Imbens\u56e0\u201c\u5bf9\u56e0\u679c\u5173\u7cfb\u5206\u6790\u7684\u65b9\u6cd5\u5b66\u8d21\u732e\u201d\u800c\u83b7\u5f972021\u5e74\u8bfa\u8d1d\u5c14\u7ecf\u6d4e\u5b66\u5956\u3002Angrist\u548cImbens\u6700\u4e3a\u77e5\u540d\u7684\u5de5\u4f5c\u662f\u5176\u572820\u4e16\u7eaa90\u5e74\u4ee3\u5c06\u5de5\u5177\u53d8\u91cf\u5f15\u5165\u4e86\u6f5c\u5728\u7ed3\u679c\u6846\u67b6\uff0c\u8be5\u6846\u67b6\u4e5f\u88ab\u79f0\u4e3aRubin\u56e0\u679c\u6a21\u578b\u3002\u672c\u6b21\u56e0\u679c\u79d1\u5b66\u7b2c\u4e09\u5b63\u8bfb\u4e66\u4f1a<\/a>\u7b2c\u4e00\u671f\u9080\u8bf7\u5230\u4e86\u8be5\u6846\u67b6\u7684\u63d0\u51fa\u8005\uff0c\u7edf\u8ba1\u5b66\u5bb6Donald B. Rubin\u6559\u6388\u6765\u4e3a\u6211\u4eec\u4ecb\u7ecd\u6f5c\u5728\u7ed3\u679c\u6846\u67b6\uff0c\u6b22\u8fce\u70b9\u51fb\u6587\u672b\u4e86\u89e3\u8be6\u60c5\u3002<\/span><\/strong><\/span><\/p>\n


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Donald B. Rubin\u6559\u6388\uff0c\u7f8e\u56fd\u56fd\u5bb6\u79d1\u5b66\u9662\u9662\u58eb\uff0c\u7f8e\u56fd\u79d1\u5b66\u4e0e\u827a\u672f\u5b66\u9662\u9662\u58eb\uff0c\u66fe\u4efb\u54c8\u4f5b\u5927\u5b66\u7edf\u8ba1\u7cfbJohn L. Loeb\u8bb2\u5e2d\u6559\u6388\uff0c\u73b0\u4efb\u6e05\u534e\u5927\u5b66\u4e18\u6210\u6850\u6570\u5b66\u79d1\u5b66\u4e2d\u5fc3\u6559\u6388\u3002\u4ed6\u83b7\u5f97\u8fc7\u7edf\u8ba1\u5b66\u9886\u57df\u51e0\u4e4e\u6240\u6709\u8457\u540d\u5956\u9879\uff0c\u5305\u62ec\u8457\u540d\u7684 Wilks\u5956\u7ae0\u3001Parzen\u5956\u3001Snedecor\u5956\u7b49\uff0c\u662f\u5f53\u4eca\u4e16\u754c\u6700\u5177\u5f71\u54cd\u529b\u7684\u7edf\u8ba1\u5b66\u6cf0\u6597\u3002\u4ed6\u5bf9\u79d1\u5b66\u7684\u8d21\u732e\u5df2\u8d85\u51fa\u7edf\u8ba1\u5b66\u8303\u7574\uff0c\u5176\u7edf\u8ba1\u601d\u60f3\u5bf9\u751f\u7269\u533b\u5b66\u3001\u7ecf\u6d4e\u5b66\u3001\u5fc3\u7406\u5b66\u3001\u6559\u80b2\u5b66\u3001\u793e\u4f1a\u5b66\u53ca\u8ba1\u7b97\u673a\u79d1\u5b66\u7b49\u4f17\u591a\u9886\u57df\u4ea7\u751f\u4e86\u5212\u65f6\u4ee3\u7684\u5f71\u54cd\uff0c\u8c37\u6b4c\u5b66\u672f\u663e\u793a\u5176\u6587\u7ae0\u548c\u8457\u4f5c\u5f15\u7528\u91cf\u5df2\u8d85\u8fc735\u4e07\u6b21\u3002<\/span><\/strong><\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\u5c3d\u7ba1\u4ece\u6700\u521d\u7ea7\u7684\u7edf\u8ba1\u8bfe\u5f00\u59cb\uff0c\u6211\u4eec\u5c31\u88ab\u53cd\u590d\u6559\u5bfc\u201c\u76f8\u5173\u4e0d\u610f\u5473\u7740\u56e0\u679c\u201d\uff0c\u4f46\u5728\u65e5\u5e38\u751f\u6d3b\u4e2d\uff0c\u6211\u4eec\u8fd8\u662f\u7ecf\u5e38\u4f7f\u7528\u201c\u56e0\u679c\u201d\u7684\u8bed\u8a00\u6765\u63cf\u8ff0\u6211\u4eec\u7684\u7ecf\u5386\u3002\u4f8b\u5982\uff1a\u201c\u6211\u4eca\u5929\u611f\u5192\u597d\u4e86\u662f\u56e0\u4e3a\u6211\u5403\u4e86\u963f\u83ab\u897f\u6797\u201d\uff0c\u201c\u4ed6\u8003\u8bd5\u6ca1\u53ca\u683c\u662f\u56e0\u4e3a\u4ece\u6765\u4e0d\u505a\u4f5c\u4e1a\u201d\uff0c\u6216\u8005\u201c\u7f8e\u56fd\u7684\u65b0\u51a0\u75c5\u4f8b\u6570\u51fa\u73b0\u53cd\u5f39\u662f\u56e0\u4e3a\u51fa\u73b0\u4e86\u5fb7\u5c14\u5854\u53d8\u5f02\u682a\u201d\u3002\u4f46\u662f\u540c\u65f6\uff0c\u6211\u4eec\u4f3c\u4e4e\u4e5f\u80fd\u533a\u5206\u76f8\u5173\u6027\u4e0e\u56e0\u679c\u6027\uff0c\u6bd4\u5982\u6ca1\u6709\u4eba\u4f1a\u4e3b\u5f20\u201c\u592a\u9633\u5347\u8d77\u662f\u56e0\u4e3a\u9e21\u6253\u9e23\u4e86\u201d\u3002<\/span><\/p>\n


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\u5728\u65e5\u5e38\u751f\u6d3b\u4e2d\uff0c\u6211\u4eec\u4f9d\u8d56\u81ea\u5df1\u7684\u7ecf\u9a8c\u4ee5\u53ca\u5e38\u8bc6\u6765\u5224\u65ad\u56e0\u679c\u6216\u76f8\u5173\u5173\u7cfb\u3002\u4f46\u662f\u5728\u79d1\u5b66\u7814\u7a76\u4e2d\uff0c\u4eba\u4eec\u9762\u5bf9\u7684\u5f80\u5f80\u662f\u672a\u77e5\u7684\u4e8b\u7269\uff0c\u7ecf\u9a8c\u6216\u8005\u5e38\u8bc6\u53d8\u5f97\u4e0d\u518d\u53ef\u9760\u3002\u957f\u671f\u4ee5\u6765\uff0c\u79d1\u5b66\u5bb6\u4eec\u4f9d\u8d56\u968f\u673a\u5bf9\u7167\u5b9e\u9a8c\u6765\u7814\u7a76\u56e0\u679c\u5173\u7cfb\u3002\u8b6c\u5982\u5982\u679c\u8981\u7814\u7a76\u67d0\u79cd\u836f\u7269\u5bf9\u6cbb\u7597\u75be\u75c5\u7684\u5f71\u54cd\uff0c\u9700\u8981\u5c06\u75c5\u4eba\u968f\u673a\u5730\u5206\u4e3a\u4e24\u7ec4\uff0c\u5206\u522b\u7ed9\u4e88\u836f\u7269\u53ca\u5b89\u6170\u5242\uff0c\u5e76\u4f9d\u6b64\u6bd4\u8f83\u4e24\u7ec4\u95f4\u7684\u7ed3\u5c40\u5dee\u5f02\u3002\u7136\u800c\uff0c\u5728\u73b0\u5b9e\u4e2d\uff0c\u968f\u673a\u5bf9\u7167\u5b9e\u9a8c\u5e76\u4e0d\u603b\u662f\u53ef\u884c\u7684\u3002\u4f8b\u5982\uff0c\u5982\u679c\u6211\u4eec\u8981\u7814\u7a76\u5438\u70df\u4e0e\u80ba\u764c\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u6211\u4eec\u4e0d\u53ef\u80fd\u5c06\u4eba\u7fa4\u968f\u673a\u5206\u4e3a\u4e24\u7ec4\uff0c\u4e00\u7ec4\u8ba9\u5176\u5438\u70df\u3001\u4e00\u7ec4\u8ba9\u5176\u4e0d\u5438\uff0c\u56e0\u4e3a\u8fd9\u4e0d\u7b26\u5408\u4f26\u7406\u3002\u540c\u6837\uff0c\u6211\u4eec\u60f3\u7814\u7a76\u63a5\u53d7\u5927\u5b66\u6559\u80b2\u5bf9\u4e00\u4e2a\u4eba\u6536\u5165\u7684\u5f71\u54cd\uff0c\u4e5f\u4e0d\u80fd\u968f\u673a\u5730\u8ba9\u53d7\u8bd5\u8005\u4e0a\u5927\u5b66\u6216\u4e0d\u4e0a\u5927\u5b66\u3002\u57fa\u4e8e\u968f\u673a\u5bf9\u7167\u5b9e\u9a8c\u6240\u5b9a\u4e49\u7684\u56e0\u679c\u5173\u7cfb\u5728\u73b0\u5b9e\u4e2d\u6709\u5f88\u5927\u7684\u5c40\u9650\u6027\u3002\u6211\u4eec\u9700\u8981\u4e00\u79cd\u5f62\u5f0f\u5316\u7684\u56e0\u679c\u7684\u5b9a\u4e49\uff0c\u4f7f\u5176\u53ef\u4ee5\u5c3d\u53ef\u80fd\u5e7f\u6cdb\u5730\u7528\u4e8e\u5404\u79cd\u7814\u7a76\u7c7b\u578b\u4e2d\uff0c\u73b0\u5982\u4eca\u5728\u7edf\u8ba1\u5b66\u3001\u7ecf\u6d4e\u5b66\u3001\u6d41\u884c\u75c5\u5b66\u4ee5\u53ca\u5176\u4ed6\u81ea\u7136\u53ca\u793e\u4f1a\u79d1\u5b66\u4e2d\u88ab\u5e7f\u6cdb\u4f7f\u7528\u7684\u6f5c\u5728\u7ed3\u679c<\/span>\uff08potential outcome\uff09<\/span>\u6846\u67b6\uff0c\u5c31\u662f\u8fd9\u6837\u7684\u4e00\u79cd\u5f62\u5f0f\u5316\u7684\u5b9a\u4e49\u3002<\/span><\/p>\n


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\u6f5c\u5728\u7ed3\u679c\u6700\u521d\u7684\u63d0\u51fa\u662f\u5728Neyman\u7684\u8bba\u6587[1]\u4e2d\uff0c\u4f46\u662f\u8fd9\u7bc7\u6587\u7ae0\u53ea\u5728\u968f\u673a\u5bf9\u7167\u8bd5\u9a8c\u4e2d\u4f7f\u7528\u4e86\u6f5c\u5728\u7ed3\u679c\u7684\u6982\u5ff5\uff0c\u4e14\u76f4\u52301990\u5e74\u7ffb\u8bd1\u6210\u82f1\u6587\u540e\u624d\u4e3a\u4eba\u6240\u77e5\u3002Rubin\u5728\u4ed61974\u5e74\u7684\u8bba\u6587\u4e2d\u4e5f\u63d0\u51fa\u4e86\u6f5c\u5728\u7ed3\u679c\u7684\u6982\u5ff5\uff0c\u5e76\u5c06\u8fd9\u4e2a\u6982\u5ff5\u63a8\u5e7f\u5230\u4e86\u89c2\u5bdf\u6027\u6570\u636e\u4e2d[2]\uff0c\u771f\u6b63\u5f00\u542f\u4e86\u7edf\u8ba1\u5b66\u754c\u5bf9\u56e0\u679c\u63a8\u65ad\u7684\u5e7f\u6cdb\u7814\u7a76\u3002\u56e0\u6b64\u6f5c\u5728\u7ed3\u679c\u6846\u67b6\u6709\u65f6\u4e5f\u88ab\u79f0\u4e3aRubin\u56e0\u679c\u6a21\u578b[3]\u3002<\/span><\/p>\n


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\u4f55\u4e3a\u6f5c\u5728\u7ed3\u679c\uff1f\u53c8\u5982\u4f55\u57fa\u4e8e\u6f5c\u5728\u7ed3\u679c\u5b9a\u4e49\u56e0\u679c\uff1f\u5047\u8bbe\u6211\u4eec\u5173\u5fc3\u67d0\u4e2a\u53d8\u91cfA<\/span>\uff08\u4f8b\u5982\uff0c\u5728\u67d0\u4e2a\u65f6\u95f4\u70b9\u662f\u5426\u670d\u7528\u963f\u83ab\u897f\u6797\uff0cA=1\u662f\u670d\u7528\uff0cA=0\u662f\u6ca1\u6709\u670d\u7528\uff09<\/span>\u5bf9Y<\/span>\uff08\u670d\u7528\u540e\u4e09\u5c0f\u65f6\u7684\u662f\u5426\u8fd8\u611f\u5192\uff0cY=1\u8868\u793a\u611f\u5192\uff0cY=0\u8868\u793a\u6ca1\u6709\u611f\u5192\uff09<\/span>\u7684\u56e0\u679c\u5173\u7cfb\u3002\u90a3\u4e48\u6211\u4eec\u89c2\u5bdf\u5230\u7684\u67d0\u4e2a\u4e2a\u4f53\u5c31\u5b58\u5728\u4e24\u4e2a\u201c\u6f5c\u5728\u201d\u7684\u72b6\u6001\uff1a\u4e00\u4e2a\u662f\u5982\u679c\u4ed6\u670d\u836f\uff0c\u4ed6\u4e09\u5c0f\u65f6\u540e\u662f\u5426\u611f\u5192\uff0c\u4e0d\u59a8\u8bb0\u4f5cY(1)\uff1b\u53e6\u4e00\u4e2a\u5982\u679c\u4ed6\u6ca1\u6709\u670d\u836f\uff0c\u4ed6\u4e09\u5c0f\u65f6\u540e\u662f\u5426\u611f\u5192\uff0c\u4e0d\u59a8\u8bb0\u4f5cY(0)\u3002\u8fd9\u91ccY(1)\u548cY(0)\u5c31\u662f\u6f5c\u5728\u7ed3\u679c\u3002<\/span>\uff08\u6ce8\u610f\uff0c\u5728\u5b9e\u9645\u4e2d\uff0cY(1)\u548cY(0)\u8fd9\u4e8c\u8005\u4e2d\u53ea\u6709\u4e00\u4e2a\u53ef\u4ee5\u88ab\u89c2\u5bdf\u5230\u3002\u53e6\u5916\uff0c\u4e25\u683c\u5730\u8bf4\uff0c\u6b64\u5904\u5b9e\u9645\u4e0a\u505a\u4e86\u201c\u4e2a\u4f53\u5904\u7406\u503c\u7a33\u5b9a\u201d\u5373SUTVA\u7684\u5047\u8bbe\uff09<\/span>\u90a3\u4e48\u5bf9\u8fd9\u4e2a\u4eba\uff0c\u5c31\u53ef\u80fd\u6709\u4ee5\u4e0b\u56db\u79cd\u60c5\u51b5\uff1a<\/span><\/p>\n


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a) Y(0)=0, Y(1)=0\u3002\u5373\u4e0d\u8bba\u5403\u4e0d\u5403\u836f\uff0c\u8fd9\u4e2a\u4eba\u5728\u4e09\u5c0f\u65f6\u540e\u5747\u4e0d\u4f1a\u611f\u5192\u3002<\/span><\/section>\n
b) Y(0)=1, Y(1)=1\u3002\u5373\u4e0d\u8bba\u5403\u4e0d\u5403\u836f\uff0c\u8fd9\u4e2a\u4eba\u5728\u4e09\u5c0f\u65f6\u540e\u5747\u4f1a\u611f\u5192\u3002<\/span><\/section>\n
c) Y(0)=1, Y(1)=0\u3002\u5373\u6b64\u4eba\u5982\u679c\u4e0d\u5403\u836f\uff0c\u4e09\u5c0f\u65f6\u540e\u4f1a\u611f\u5192\uff0c\u4f46\u662f\u5982\u679c\u5403\u836f\uff0c\u4e09\u5c0f\u65f6\u540e\u4e0d\u4f1a\u611f\u5192\u3002<\/span><\/section>\n

d) Y(0)=0, Y(1)=1\u3002\u5373\u6b64\u4eba\u5982\u679c\u4e0d\u5403\u836f\uff0c\u4e09\u5c0f\u65f6\u540e\u4e0d\u4f1a\u611f\u5192\uff0c\u4f46\u662f\u5982\u679c\u5403\u836f\uff0c\u4e09\u5c0f\u65f6\u540e\u4f1a\u611f\u5192\u3002<\/span><\/p>\n


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\u5728a\u548cb\u4e24\u79cd\u60c5\u51b5\u4e0b\uff0cY(1)=Y(0)\uff0c\u5373\u5403\u4e0d\u5403\u836f\u4e0d\u4f1a\u5f71\u54cd\u4e09\u5c0f\u65f6\u540e\u662f\u5426\u611f\u5192\u7684\u72b6\u6001\uff0c\u8fd9\u79cd\u60c5\u51b5\u4e0b\u6211\u4eec\u8bf4\u5403\u836f\u5bf9\u4e09\u5c0f\u65f6\u540e\u662f\u5426\u611f\u5192\u6ca1\u6709\u56e0\u679c\u4f5c\u7528\uff0c\u76f8\u53cd\uff0c\u5728c\u548cd\u4e24\u79cd\u60c5\u51b5\u4e0b\uff0cY(1)\u2260Y(0)\uff0c\u8fd9\u79cd\u60c5\u51b5\u4e0b\u6211\u4eec\u8bf4\u5403\u836f\u5bf9\u4e09\u5c0f\u65f6\u540e\u662f\u5426\u611f\u5192\u6709\u56e0\u679c\u4f5c\u7528\u3002\u4f7f\u7528\u6f5c\u5728\u7ed3\u679c\uff0c\u6211\u4eec\u4fbf\u53ef\u4ee5\u65b9\u4fbf\u5730\u5b9a\u4e49\u611f\u5174\u8da3\u7684\u56e0\u679c\u4f5c\u7528\uff0c\u4f8b\u5982\u5e73\u5747\u56e0\u679c\u6548\u5e94E[Y(1)-Y(0)]\uff0c\u8fd9\u4e2a\u91cf\u4ee3\u8868\u4e86\u5728\u4e00\u4e2a\u7fa4\u4f53\u4e2d\uff0c\u5982\u679c\u6bcf\u4e00\u4e2a\u4eba\u90fd\u91c7\u53d6\u67d0\u79cd\u5904\u7406\u548c\u90fd\u4e0d\u63a5\u53d7\u5904\u7406\u76f8\u6bd4\uff0c\u8fd9\u4e24\u79cd\u60c5\u51b5\u4e0b\u5e73\u5747\u610f\u4e49\u4e0a\u7684\u7ed3\u679c\u5dee\u503c\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u4f7f\u7528\u6f5c\u5728\u7ed3\u679c\u6211\u4eec\u6216\u8bb8\u53ef\u4ee5\u7406\u89e3\u4e3a\u4ec0\u4e48\u4eba\u4eec\u4e0d\u4f1a\u8ba4\u4e3a\u201c\u592a\u9633\u5347\u8d77\u662f\u56e0\u4e3a\u9e21\u6253\u9e23\u201d\u4e86\uff0c\u56e0\u4e3a\u6839\u636e\u6211\u4eec\u7684\u5e38\u8bc6\uff0c\u5982\u679c\u67d0\u5929\u9e21\u4e0d\u6253\u9e23<\/span>\uff08\u6216\u8bb8\u662f\u56e0\u4e3a\u751f\u75c5\u6216\u52b3\u7d2f\uff09<\/span>\uff0c\u592a\u9633\u4ecd\u7136\u4f1a\u7167\u5e38\u5347\u8d77\u3002<\/span><\/p>\n


<\/p>\n

 <\/span>
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<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

\u4e8c\u300120\u4e16\u7eaa80\u5e74\u4ee3\uff1a\u503e\u5411\u6027\u8bc4\u5206\u7684\u63d0\u51fa<\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

Rubin\u7684\u53e6\u4e00\u91cd\u5927\u7684\u8d21\u732e\u5219\u662f\u548cRosenbaum\u4e00\u8d77\u63d0\u51fa\u4e86\u503e\u5411\u6027\u8bc4\u5206\u7684\u6982\u5ff5 [4]\u3002\u4ed6\u4eec\u7684\u8fd9\u7bc7\u6587\u7ae0\u662f\u8457\u540d\u7edf\u8ba1\u5b66\u671f\u520aBiometrika\u5f15\u7528\u91cf\u6700\u9ad8\u7684\u6587\u7ae0\u4e4b\u4e00\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u968f\u673a\u8bd5\u9a8c\u4e4b\u6240\u4ee5\u88ab\u8ba4\u4e3a\u662f\u56e0\u679c\u63a8\u65ad\u7684\u91d1\u6807\u51c6\uff0c\u5f88\u5927\u7a0b\u5ea6\u4e0a\u662f\u56e0\u4e3a\u5176\u5904\u7406\u662f\u968f\u673a\u5206\u914d\u7684\uff0c\u800c\u4e0d\u662f\u7531\u53d7\u8bd5\u8005\u81ea\u5df1\u9009\u62e9\u7684\u3002\u5904\u7406\u662f\u968f\u673a\u5206\u914d\u7684\u5047\u8bbe\u53ef\u4ee5\u5f62\u5f0f\u5316\u5730\u8868\u8fbe\u4e3aA\u22a5{Y(0),Y(1)}\u3002\u5728\u8fd9\u6761\u5047\u8bbe\u4e0b\uff0c\u6211\u4eec\u53ef\u4ee5\u8bf4\u660e\uff0c\u57fa\u4e8e\u89c2\u5bdf\u6570\u636e\u5f97\u5230\u7684\u76f8\u5173\u5173\u7cfb\u5b9e\u9645\u5c31\u53cd\u6620\u4e86\u56e0\u679c\u5173\u7cfb\uff1a<\/span><\/p>\n


<\/span><\/p>\n

E[Y(1)-Y(0)] = E[Y(1)|A=1]-E[Y(0)|A=0] = E[Y|A=1]-E[Y|A=0]<\/span><\/p>\n


<\/p>\n

\u5176\u4e2d\uff0c\u7b2c\u4e8c\u4e2a\u7b49\u53f7\u6210\u7acb\u662f\u56e0\u4e3a\u201c\u4e00\u81f4\u6027\u201d\uff0c\u5373\u5728\u67d0\u79cd\u5904\u7406\u65b9\u6848\u4e0b\u89c2\u5bdf\u5230\u7684\u7ed3\u679c\u5c31\u7b49\u4e8e\u8fd9\u79cd\u5904\u7406\u65b9\u6848\u5bf9\u5e94\u7684\u6f5c\u5728\u7ed3\u679c\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u4f46\u662f\u5728\u73b0\u5b9e\u4e2d\uff0c\u5904\u7406\u662f\u968f\u673a\u5206\u914d\u7684\u5047\u8bbe\u5f80\u5f80\u4e0d\u6210\u7acb\u3002\u4f8b\u5982\u5728\u5206\u5c42\u968f\u673a\u5316\u5b9e\u9a8c\u4e2d\uff0c\u6211\u4eec\u5148\u4f9d\u636e\u6027\u522b\u8fdb\u884c\u5206\u7ec4\uff0c\u8fdb\u800c\u5728\u6bcf\u4e2a\u7ec4\u5185\u8fdb\u884c\u968f\u673a\u5316\u5b9e\u9a8c\uff0c\u6b64\u65f6\uff0c\u6761\u4ef6\u5728\u6027\u522b\u8fd9\u4e2a\u53d8\u91cf\u4e0a\uff08\u8bb0\u4f5cX\uff09\u540e\uff0c\u5904\u7406\u7684\u5206\u914d\u662f\u968f\u673a\u7684\uff0c\u8fd9\u4e2a\u6761\u4ef6\u6211\u4eec\u53ef\u4ee5\u5199\u6210\u5982\u4e0b\u5f62\u5f0f<\/span>\uff08\u5373\u53ef\u5ffd\u7565\u6027\uff09<\/span>\uff1aA\u22a5{Y(0),Y(1)}|X\u3002\u5f88\u591a\u89c2\u5bdf\u6027\u7814\u7a76\u53ef\u4ee5\u8fd1\u4f3c\u5730\u770b\u6210\u662f\u67d0\u79cd\u5206\u5c42\u968f\u673a\u8bd5\u9a8c\uff0c\u5c3d\u7ba1\u5904\u7406\u7684\u5206\u914d\u4e0d\u662f\u968f\u673a\u7684\uff0c\u4f46\u662f\u5f53\u4e2a\u4f53\u7684\u67d0\u4e9b\u7279\u5f81\u90fd\u76f8\u540c\u65f6<\/span>\uff08\u5982\u6027\u522b\u3001\u5e74\u9f84\u3001\u6536\u5165\u7b49\uff09<\/span>\uff0c\u5904\u7406\u7684\u5206\u914d\u53ef\u4ee5\u770b\u6210\u662f\u968f\u673a\u7684\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u9488\u5bf9\u8fd9\u79cd\u89c2\u5bdf\u6027\u7814\u7a76\uff0cRubin\u6700\u521d\u7684\u60f3\u6cd5\u662f\u201c\u5339\u914d\u201d\uff0c\u5373\u5c06\u534f\u53d8\u91cfX\u76f8\u540c\u7684\u4e2a\u4f53\u653e\u5728\u4e00\u8d77\u6bd4\u8f83\uff0c\u7b97\u51fa\u5904\u7406\u7ec4\u548c\u5bf9\u7167\u7ec4\u4e4b\u95f4\u7684\u5dee\u5f02\u3002\u4f46\u662f\u8fd9\u79cd\u65b9\u6cd5\u7684\u95ee\u9898\u662f\uff0c\u5f53X\u7684\u7ef4\u5ea6\u5f88\u9ad8\u65f6\uff0c\u57fa\u4e8e\u539f\u59cb\u534f\u53d8\u91cf\u7684\u5339\u914d\u5c31\u8d8a\u6765\u8d8a\u4e0d\u73b0\u5b9e\u3002Rosenbaum\u548cRubin\u63d0\u51fa\u7684\u503e\u5411\u6027\u8bc4\u5206\uff0c\u76f8\u5f53\u4e8e\u5bf9\u539f\u59cb\u7684\u534f\u53d8\u91cf\u8fdb\u884c\u964d\u7ef4\u3002\u503e\u5411\u6027\u8bc4\u5206<\/span> (propensity score\uff0c\u8bb0\u4f5ce(X)) <\/span>\u7684\u5b9a\u4e49\u662f\uff1ae(X)=P(A=1|X)\u3002\u5b83\u5b9e\u9645\u63cf\u8ff0\u7684\u662f\u5904\u7406\u7684\u5206\u914d\u673a\u5236\u3002\u5728Rosenbaum\u548cRubin\u7684\u6587\u7ae0\u4e2d\uff0c\u4ed6\u4eec\u8bc1\u660e\u4e86A\u22a5{Y(0),Y(1)}|e(X)\uff0c\u4e8e\u662f\u53ef\u4ee5\u57fa\u4e8e\u503e\u5411\u6027\u8bc4\u5206\u8fdb\u884c\u5339\u914d\u3002\u5f53\u7136\uff0c\u5728\u73b0\u5b9e\u4e2d\uff0c\u503e\u5411\u6027\u8bc4\u5206\u5f80\u5f80\u662f\u672a\u77e5\u7684\uff0c\u9700\u8981\u8fdb\u884c\u4f30\u8ba1\u3002\u57fa\u4e8e\u503e\u5411\u6027\u8bc4\u5206\u7684\u56e0\u679c\u6548\u5e94\u7684\u4f30\u8ba1\u65b9\u6cd5\u4e5f\u6709\u5f88\u591a\uff0c\u9664\u4e86\u5339\u914d\u7684\u4f30\u8ba1\uff0c\u8fd8\u6709\u9006\u6982\u7387\u52a0\u6743\u7684\u4f30\u8ba1\uff0c\u56de\u5f52\u7684\u4f30\u8ba1\u7b49\u3002\u672c\u5c4a\u8bfa\u5956\u5f97\u4e3bImbens\u5728\u503e\u5411\u6027\u8bc4\u5206\u65b9\u6cd5\u65b9\u9762\u4e5f\u505a\u51fa\u4e86\u8bb8\u591a\u5de5\u4f5c\uff0c\u5982\u63d0\u51fa\u5e7f\u4e49\u503e\u5411\u8bc4\u5206\u7b49\u3002<\/span><\/p>\n


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\u4e09\u300120\u4e16\u7eaa90\u5e74\u4ee3\uff1a<\/strong><\/strong><\/p>\n

<\/strong><\/strong>\u5de5\u5177\u53d8\u91cf\u5f15\u5165\u6f5c\u5728\u7ed3\u679c\u6846\u67b6<\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

Rubin\u5bf9\u56e0\u679c\u63a8\u65ad\u7684\u53e6\u4e00\u8d21\u732e\u4fbf\u662f\u5c06\u5de5\u5177\u53d8\u91cf\u5f15\u5165\u4e86\u6f5c\u5728\u7ed3\u679c\u7684\u6846\u67b6\u3002\u4e3a\u4e86\u786e\u5b9a\u56e0\u679c\u6548\u5e94\uff0c\u6211\u4eec\u901a\u5e38\u9700\u8981\u5047\u8bbe\u4e0a\u8ff0\u7684\u53ef\u5ffd\u7565\u6027\u6210\u7acb\uff0c\u8fd9\u5728\u89c2\u5bdf\u6027\u7814\u7a76\u4e2d\u5f88\u96be\u6ee1\u8db3\uff0c\u5373\u5b58\u5728\u67d0\u4e9b\u89c2\u5bdf\u4e0d\u5230\u7684\u6df7\u6742\u53d8\u91cf\uff0c\u540c\u65f6\u5f71\u54cd\u5904\u7406\u5206\u914d\u548c\u7ed3\u5c40\u3002\u5728\u6709\u672a\u89c2\u6d4b\u6df7\u6742\u7684\u60c5\u51b5\u4e0b\u8bc6\u522b\u548c\u4f30\u8ba1\u56e0\u679c\u4f5c\u7528\u4e00\u76f4\u662f\u4e00\u4e2a\u5de8\u5927\u7684\u6311\u6218\u3002\u8fd9\u4e2a\u95ee\u9898\u957f\u671f\u4ee5\u6765\u4e00\u76f4\u53d7\u7ecf\u6d4e\u5b66\u5bb6\u7684\u5173\u6ce8\uff0c\u4ed6\u4eec\u957f\u671f\u4ee5\u6765\u5728\u7ebf\u6027\u7ed3\u6784\u65b9\u7a0b\u6a21\u578b\u7684\u6846\u67b6\u4e0b\u4f7f\u7528\u5de5\u5177\u53d8\u91cf\u6765\u5904\u7406\u201c\u9057\u6f0f\u53d8\u91cf\u504f\u8bef\u201d\u7684\u95ee\u9898\uff0c\u4f46\u662f\u7ebf\u6027\u7ed3\u6784\u65b9\u7a0b\u6a21\u578b\u9690\u542b\u4e86\u8f83\u5f3a\u7684\u540c\u8d28\u6027\u56e0\u679c\u6548\u5e94\u7684\u5047\u8bbe\u3002Angrist\u3001Imbens\u3001Rubin\u57281996\u5e74\u7684\u300a\u7f8e\u56fd\u7edf\u8ba1\u5b66\u4f1a\u5b66\u520a\uff08JASA\uff09\u300b\u4e0a\u53d1\u8868\u7684\u6587\u7ae0\u9996\u6b21\u5c06\u5de5\u5177\u53d8\u91cf\u5f15\u5165\u4e86\u56e0\u679c\u63a8\u65ad\u7684\u6846\u67b6\u3002\u8fd9\u4e5f\u662f\u9996\u6b21\u5728\u6f5c\u5728\u7ed3\u679c\u7684\u6846\u67b6\u4e2d\uff0c\u63d0\u51fa\u5de5\u5177\u53d8\u91cf\u7684\u4e09\u6761\u5173\u952e\u5047\u8bbe<\/span>\uff08\u6392\u4ed6\u6027\u3001\u76f8\u5173\u6027\u3001\u72ec\u7acb\u6027\uff09<\/span>\u3002\u4ed6\u4eec\u7684\u6587\u7ae0\u8fd8\u63d0\u51fa\u4e86\u4f9d\u4ece\u8005\u5e73\u5747\u56e0\u679c\u6548\u5e94\u7684\u6982\u5ff5\uff0c\u8fd9\u4e2a\u6982\u5ff5\u4e5f\u4e3a\u4e3b\u5206\u5c42\u6982\u5ff5\u7684\u63d0\u51fa\u57cb\u4e0b\u4e86\u4f0f\u7b14\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u5728Angrist\u3001Imbens\u3001Rubin\u7684\u6587\u7ae0\u91cc\uff0c\u4ed6\u4eec\u4f7f\u7528\u4e86\u4e00\u4e2a\u975e\u5e38\u5de7\u5999\u7684\u4f8b\u5b50\u3002\u8fd9\u7bc7\u6587\u7ae0\u91cc\u4ed6\u4eec\u5206\u6790\u4e86\u53c2\u519b<\/span>\uff08veteran status in the Vietnam era\uff0c\u8bb0\u4f5cA\uff09<\/span>\u5bf9\u5065\u5eb7\u7ed3\u5c40<\/span>\uff08\u8bb0\u4f5cY\uff09<\/span>\u7684\u56e0\u679c\u4f5c\u7528\u3002\u5728\u73b0\u5b9e\u4e2d\uff0c\u4e00\u4e2a\u4eba\u662f\u5426\u53c2\u519b\u5f80\u5f80\u53d7\u591a\u79cd\u56e0\u7d20\u5f71\u54cd\uff0c\u4e00\u822c\u5f88\u96be\u7a77\u5c3d\u6240\u6709\u5f71\u54cd\u53c2\u519b\u548c\u5065\u5eb7\u7ed3\u5c40\u7684\u5171\u540c\u56e0\u7d20\u3002\u4f46\u662f\u5728\u8fd9\u4e2a\u7814\u7a76\u4e2d\uff0c\u6709\u4e00\u4e2a\u5f88\u5de7\u5999\u7684\u5de5\u5177\u53d8\u91cf\u7684\u8bbe\u8ba1\uff0c\u56e0\u4e3a\u5f53\u65f6\u5165\u4f0d\u7684\u4f18\u5148\u6743\u662f\u901a\u8fc7\u968f\u673a\u5206\u914d\u7684\u901a\u8fc7\u62bd\u7b7e\u51b3\u5b9a\u7684<\/span>\uff08\u8bb0\u4f5cZ\uff09<\/span>\u3002\u7406\u8bba\u4e0a\u8bf4\uff0c\u62bd\u4e2d\u6570\u5b57\u8f83\u5c0f<\/span>\uff08Z=1\uff09<\/span>\u7684\u4eba\u5e94\u8be5\u670d\u5f79<\/span>\uff08A=1\uff09<\/span>\uff0c\u62bd\u4e2d\u6570\u5b57\u5927<\/span>\uff08Z=0\uff09<\/span>\u7684\u4eba\u4e0d\u5e94\u8be5\u670d\u5f79<\/span>\uff08A=1\uff09<\/span>\uff0c\u4f46\u662f\u5728\u73b0\u5b9e\u4e2d\uff0c\u4e5f\u4f1a\u6709\u4e0d\u4f9d\u4ece\u7684\u73b0\u8c61\u51fa\u73b0\u3002\u8fd9\u91cc\uff0cZ\u5c31\u662f\u4e00\u4e2a\u8f83\u597d\u7684\u5de5\u5177\u53d8\u91cf\uff1a\u9996\u5148\uff0c\u4e00\u4e2a\u4eba\u62bd\u4e2d\u7684\u6570\u5b57\u7684\u5927\u5c0f\u4e0d\u4f1a\u5bf9\u5065\u5eb7\u6709\u76f4\u63a5\u5f71\u54cd\uff0c\u53ea\u4f1a\u901a\u8fc7\u5f71\u54cd\u670d\u5f79<\/span>\uff08A\uff09<\/span>\u6765\u5f71\u54cd\u5065\u5eb7\uff0c\u8fd9\u6ee1\u8db3\u6392\u4ed6\u6027\u5047\u8bbe\uff1b\u5176\u6b21\uff0c\u62bd\u4e2d\u6570\u5b57\u7684\u5927\u5c0f\u4e0e\u6f5c\u5728\u7ed3\u679c\u662f\u65e0\u5173\u7684<\/span>\uff08\u56e0\u4e3a\u62bd\u7b7e\u662f\u968f\u673a\u5206\u914d\u7684\uff09<\/span>\uff0c\u8fd9\u6ee1\u8db3\u72ec\u7acb\u6027\u5047\u8bbe\uff1b\u6700\u540e\u62bd\u4e2d\u6570\u5b57\u5c0f\u7684\u4eba\u2014\u2014\u5c3d\u7ba1\u5b58\u5728\u4e0d\u4f9d\u4ece\u7684\u73b0\u8c61\u2014\u2014\u53c2\u52a0\u5175\u5f79\u7684\u53ef\u80fd\u6027\u4f1a\u66f4\u9ad8\uff0c\u5373\u76f8\u5173\u6027\u7684\u5047\u8bbe\u6210\u7acb\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u4f46\u9057\u61be\u7684\u662f\uff0c\u5373\u4f7f\u4e0a\u8ff0\u4e09\u4e2a\u6761\u4ef6\u5747\u6210\u7acb\uff0c\u5de5\u5177\u53d8\u91cf\u4f9d\u7136\u4e0d\u8db3\u4ee5\u8bc6\u522b\u6211\u4eec\u901a\u5e38\u611f\u5174\u8da3\u7684\u56e0\u679c\u53c2\u6570<\/span>\uff08\u5982\u5e73\u5747\u56e0\u679c\u6548\u5e94\uff09<\/span>\u3002\u6ce8\u610f\u5230\u4eba\u7fa4\u4e2d\u5b58\u5728\u56db\u79cd\u4eba\uff0c\u6211\u4eec\u4e00\u4e00\u5217\u51fa\u5982\u4e0b<\/span>\uff08\u6b64\u5904A\u5199\u6210Z\u7684\u6f5c\u5728\u7ed3\u679c\uff09<\/span>\uff1a<\/span><\/p>\n


<\/span><\/p>\n

a) A(0)=0, A(1)=0\u3002\u5373\u65e0\u8bba\u62bd\u7b7e\u5927\u5c0f\uff0c\u5747\u4e0d\u670d\u5175\u5f79\u3002<\/span><\/section>\n
b) A(0)=1, A(1)=1\u3002\u5373\u65e0\u8bba\u62bd\u7b7e\u5927\u5c0f\uff0c\u5747\u670d\u5175\u5f79\u3002<\/span><\/section>\n
c) A(1)=1, A(0)=0\u3002\u5373\u5982\u679c\u62bd\u7b7e\u62bd\u4e2d\uff0c<\/span>\uff08\u5373\u62bd\u7b7e\u7684\u6570\u5b57\u5c0f\uff0cZ=1\uff09<\/span>\u5c31\u53bb\u670d\u5175\u5f79\uff0c\u53cd\u4e4b\u4e0d\u670d\u5175\u5f79\u3002<\/span><\/section>\n

d) A(0)=1, A(1)=0\u3002\u5373\u5982\u679c\u62bd\u7b7e\u6ca1\u62bd\u4e2d\uff0c<\/span>\uff08\u5373\u62bd\u7b7e\u7684\u6570\u5b57\u5c0f\uff0cZ=1\uff09<\/span>\u5c31\u53bb\u670d\u5175\u5f79\uff0c\u53cd\u4e4b\u4e0d\u670d\u5175\u5f79\u3002<\/span><\/p>\n


<\/p>\n

\u5728Angrist\u3001Imbens\u3001Rubin\u7684\u6587\u7ae0\u91cc\uff0c\u4ed6\u4eec\u5047\u8bbe\u7b2c\u56db\u79cd\u4eba\u662f\u4e0d\u5b58\u5728\u7684\uff0c\u5373\u201c\u5355\u8c03\u6027\u201d\u5047\u8bbe\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u4eba\u7fa4\u4e2d\u6ca1\u6709\u8fd9\u79cd\u770b\u4f3c\u975e\u5e38\u5947\u602a\u7684\u4eba\uff0c\u4ed6\u4eec\u5982\u679c\u6ca1\u88ab\u62bd\u4e2d\u5c31\u56de\u53bb\u670d\u5175\u5f79\uff0c\u4f46\u662f\u88ab\u62bd\u4e2d\u7684\u5c31\u4e0d\u53bb\u670d\u5175\u5f79\u3002\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u5355\u8c03\u6027\u4f3c\u4e4e\u662f\u4e00\u4e2a\u5f88\u6709\u9053\u7406\u7684\u5047\u8bbe\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u5728\u4ee5\u4e0a\u7684\u5047\u8bbe\u4e0b\uff0cAngrist\u3001Imbens\u3001Rubin\u63d0\u51fa\u4e86\u4f9d\u4ece\u8005\uff08\u5373\u7b2cc\u7c7b\u4eba\uff09\u7684\u5e73\u5747\u56e0\u679c\u6548\u5e94\u662f\u53ef\u4ee5\u8bc6\u522b\u7684\uff0c\u800c\u4e14\u5c31\u7b49\u4e8e\u5982\u4e0b\u7684Wald\u4f30\u8ba1\u91cf\uff1a<\/span><\/p>\n


<\/span><\/p>\n

E[Y(1)-Y(0)|A(1)=1,A(0)=0] = {E[Y|Z=1]-E[Y|Z=0]}\/{E[A|Z=1]-E[A|Z=0]}<\/span><\/p>\n


<\/span><\/p>\n

\u8fd9\u4e2a\u91cf\u88ab\u79f0\u4f5c\u5c40\u90e8\u5e73\u5747\u56e0\u679c\u4f5c\u7528<\/span>\uff08LATE\uff09<\/span>\uff0c\u4e5f\u88ab\u79f0\u4f5c\u4f9d\u4ece\u8005\u5e73\u5747\u56e0\u679c\u4f5c\u7528<\/span>\uff08CACE\uff09<\/span>\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u540c\u4e00\u822c\u7684\u5728\u8ba1\u91cf\u4e2d\u88ab\u5e7f\u6cdb\u4f7f\u7528\u7684\u201c\u5de5\u5177\u53d8\u91cf\u56de\u5f52\u201d\uff0cAngrist\u3001Imbens\u3001Rubin\u7684\u65b9\u6cd5\u51e0\u4e4e\u6ca1\u6709\u4efb\u4f55\u7684\u6a21\u578b\u5047\u8bbe\u3002\u6b64\u540e\uff0c\u5bf9\u4e8e\u5904\u7406\u672a\u89c2\u6d4b\u6df7\u6742\u7684\u65b9\u6cd5\u4ee5\u53ca\u5de5\u5177\u53d8\u91cf\u65b9\u6cd5\u7684\u7814\u7a76\u53d8\u6210\u4e86\u56e0\u679c\u63a8\u65ad\u4e2d\u7684\u4e00\u4e2a\u91cd\u8981\u9886\u57df\u3002<\/span><\/p>\n


<\/p>\n

 <\/span>
<\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

\u56db\u3001\u65b0\u5343\u5e74\uff1a\u4e3b\u5206\u5c42\u6982\u5ff5\u7684\u63d0\u51fa<\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

\u524d\u9762\u63d0\u5230\uff0c\u5728\u4ece\u5728\u975e\u4f9d\u4ece\u73b0\u8c61\u65f6\uff0c\u6211\u4eec\u80fd\u591f\u8bc6\u522b\u7684\u53ea\u662f\u4f9d\u4ece\u8005\u2014\u2014\u4e5f\u5c31\u662f\u4eba\u7fa4\u4e2d\u7684\u67d0\u4e00\u201c\u5c42\u201d\u2014\u2014\u7684\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u3002Frangakis\u548cRubin\u628a\u8fd9\u4e00\u89c2\u5bdf\u603b\u7ed3\u4e3a\u4e3b\u5206\u5c42<\/span>\uff08principal stratification\uff09<\/span>\u7684\u6982\u5ff5[6]\uff0c\u5373\u6309\u7167\u67d0\u79cd\u5904\u7406\u540e\u7684\u6f5c\u5728\u7ed3\u679c\u5bf9\u603b\u4f53\u8fdb\u884c\u5206\u5c42\uff0c\u800c\u771f\u6b63\u5173\u5fc3\u7684\u56e0\u679c\u4f5c\u7528\u88ab\u5c40\u9650\u5728\u67d0\u4e00\u4e2a\u4e3b\u5c42\u5185\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u8003\u8651\u4e00\u9879\u6fc0\u52b1\u8bd5\u9a8c\uff0c\u533b\u751f\u968f\u673a\u5730\u9f13\u52b1\u6216\u4e0d\u9f13\u52b1\u60a3\u8005\u6253\u75ab\u82d7\u3002\u5b9e\u9645\u4e0a\uff0c\u60a3\u8005\u5373\u4f7f\u88ab\u9f13\u52b1\u6253\u75ab\u82d7\u4e86\uff0c\u4ed6\u4e5f\u6709\u53ef\u80fd\u4e0d\u6253\u75ab\u82d7\uff0c\u800c\u6ca1\u6709\u88ab\u9f13\u52b1\u7684\u60a3\u8005\u4e5f\u53ef\u80fd\u81ea\u5df1\u53bb\u6253\u75ab\u82d7\u4e86\u3002\u7528Z\u8868\u793a\u533b\u751f\u662f\u5426\u9f13\u52b1\u60a3\u8005\u6253\u75ab\u82d7<\/span>\uff08Z=1\u8868\u793a\u9f13\u52b1\uff0cZ=0\u8868\u793a\u4e0d\u9f13\u52b1\uff09<\/span>\uff0c\u7528A\u8868\u793a\u60a3\u8005\u5b9e\u9645\u4e0a\u662f\u5426\u6253\u4e86\u75ab\u82d7<\/span>\uff08A=1\u8868\u793a\u6253\u75ab\u82d7\u4e86\uff0cA=0\u8868\u793a\u6ca1\u6709\u6253\u75ab\u82d7\uff09<\/span>\uff0c\u7528Y\u8868\u793a\u60a3\u8005\u662f\u5426\u5f97\u4e86\u6d41\u611f<\/span>\uff08Y=1\u8868\u793a\u5f97\u6d41\u611f\uff0cY=0\u8868\u793a\u6ca1\u6709\u5f97\u6d41\u611f\uff09<\/span>\u3002\u6ce8\u610f\u5230A\u53ef\u4ee5\u8868\u793a\u4e3aZ\u7684\u6f5c\u5728\u7ed3\u679c\uff0c\u8bb0\u4e3aA(z)\uff1bY\u53ef\u4ee5\u8868\u793a\u4e3aZ\u548cA\u7684\u6f5c\u5728\u7ed3\u679c\uff0c\u8bb0\u4e3aY(z,a)\u3002\u6211\u4eec\u53ef\u4ee5\u6839\u636eA(z)\u628a\u4eba\u7fa4\u5206\u4e3a\u56db\u5c42\uff1a<\/span><\/p>\n


<\/span><\/p>\n

a) A(0)=0, A(1)=0\u3002\u5373\u65e0\u8bba\u533b\u751f\u662f\u5426\u9f13\u52b1\u6253\u75ab\u82d7\uff0c\u60a3\u8005\u90fd\u4e0d\u4f1a\u6253\u75ab\u82d7\uff0c\u79f0\u8fd9\u4e9b\u4eba\u4e3a\u62d2\u4e0d\u670d\u836f\u8005\u3002<\/span><\/section>\n
b) A(0)=1, A(1)=1\u3002\u5373\u65e0\u8bba\u533b\u751f\u662f\u5426\u9f13\u52b1\u6253\u75ab\u82d7\uff0c\u60a3\u8005\u90fd\u4f1a\u6253\u75ab\u82d7\uff0c\u79f0\u8fd9\u4e9b\u4eba\u4e3a\u6c38\u8fdc\u670d\u836f\u8005\u3002<\/span><\/section>\n
c) A(1)=1, A(0)=0\u3002\u5373\u60a3\u8005\u4f1a\u6309\u7167\u533b\u751f\u7684\u5efa\u8bae\u6253\u75ab\u82d7\uff0c\u79f0\u8fd9\u4e9b\u4eba\u4e3a\u4f9d\u4ece\u8005\u3002<\/span><\/section>\n

d) A(0)=1, A(1)=0\u3002\u5373\u60a3\u8005\u4f1a\u505a\u51fa\u4e0e\u533b\u751f\u5efa\u8bae\u76f8\u53cd\u7684\u51b3\u7b56\uff0c\u79f0\u8fd9\u4e9b\u4eba\u4e3a\u62b5\u6297\u8005\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u5047\u8bbe\u6392\u4ed6\u6027\u6210\u7acb\uff0c\u5373Y(0,a)=Y(1,a)\uff0c\u4e00\u4e2a\u4eba\u662f\u5426\u4f1a\u5f97\u6d41\u611f\u53ea\u4f9d\u8d56\u4e8e\u4ed6\u6709\u6ca1\u6709\u6253\u75ab\u82d7\uff0c\u4e0e\u533b\u751f\u662f\u5426\u9f13\u52b1\u4ed6\u5e76\u4e0d\u76f4\u63a5\u76f8\u5173\u3002\u7a0d\u52a0\u89c2\u5bdf\u6211\u4eec\u5c31\u4f1a\u53d1\u73b0\uff0c\u7b2ca\u7ec4\u4eba\u548c\u7b2cb\u7ec4\u4eba\u5bf9\u4e8e\u4f30\u8ba1\u6253\u75ab\u82d7\u7684\u771f\u6b63\u4f5c\u7528\u662f\u6ca1\u6709\u5e2e\u52a9\u7684\uff0c\u56e0\u4e3a\u4ed6\u4eec\u5f97\u6d41\u611f\u7684\u6f5c\u5728\u7ed3\u679c\u90fd\u76f8\u7b49\uff0c\u8981\u4e48\u90fd\u662fY(0)\uff0c\u8981\u4e48\u90fd\u662fY(1)\u3002\u53ea\u6709\u7b2cc\u7ec4\u4eba\u548c\u7b2cd\u7ec4\u4eba\u5bf9\u4e8e\u4f30\u8ba1\u6253\u75ab\u82d7\u7684\u771f\u6b63\u56e0\u6545\u4f5c\u7528\u6709\u5e2e\u52a9\uff0c\u56e0\u4e3a\u5bf9\u4e8e\u8fd9\u4e24\u7ec4\u4eba\u6765\u8bf4\uff0c\u6bcf\u4e00\u7ec4\u5185\u540c\u65f6\u5b58\u5728\u6253\u75ab\u82d7\u7684\u4eba\u548c\u4e0d\u6253\u75ab\u82d7\u7684\u4eba\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u533b\u5b66\u4e0a\u5e38\u7528\u610f\u5411\u6cbb\u7597\u7b56\u7565\u6765\u63cf\u8ff0\u6fc0\u52b1\u8bd5\u9a8c\uff0c\u7528E[Y|Z=1]-E[Y|Z=0]\u6765\u63cf\u8ff0\u9f13\u52b1\u60a3\u8005\u6253\u75ab\u82d7\u5e26\u6765\u7684\u4f5c\u7528\u3002\u7136\u800c\uff0c\u8fd9\u4e2a\u91cf\u5e76\u6ca1\u6709\u56e0\u679c\u89e3\u91ca\uff0c\u5b83\u5e76\u4e0d\u80fd\u53cd\u6620\u6253\u75ab\u82d7\u7684\u56e0\u679c\u4f5c\u7528\u3002\u5229\u7528\u4e3b\u5206\u5c42\u7684\u6846\u67b6\uff0c\u6211\u4eec\u5c31\u80fd\u6e05\u695a\u5730\u770b\u5230\uff0c\u53ea\u6709\u5728\u4f9d\u4ece\u8005\u6216\u62b5\u6297\u8005\u8fd9\u4e24\u4e2a\u4eba\u7fa4\u4e0a\u624d\u80fd\u5b9a\u4e49\u56e0\u679c\u4f5c\u7528\u3002\u5982\u679c\u518d\u5047\u8bbe\u5355\u8c03\u6027\uff0c\u8ba4\u4e3a\u62b5\u6297\u8005\u4e0d\u5b58\u5728\uff0c\u90a3\u4e48\u611f\u5174\u8da3\u7684\u56e0\u679c\u91cf\u5c31\u53ea\u80fd\u5728\u4f9d\u4ece\u8005\u4e2d\u5b9a\u4e49\u4e86\uff0c\u8fd9\u4e2a\u91cf\u4e5f\u5c31\u662f\u524d\u9762\u63d0\u5230\u7684\u4f9d\u4ece\u8005\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u4e86\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u5f53\u7136\uff0c\u4e3b\u5206\u5c42\u4e5f\u80fd\u5904\u7406\u975e\u4f9d\u4ece\u4ee5\u5916\u7684\u95ee\u9898\u3002\u5047\u8bbe\u6211\u4eec\u60f3\u8981\u77e5\u9053\u67d0\u79cd\u6cbb\u7597\u65b9\u6848\u5bf9\u4e8e\u60a3\u8005\u751f\u6d3b\u8d28\u91cf\u7684\u6539\u5584\u60c5\u51b5\uff0c\u8bb0Z\u4e3a\u6cbb\u7597\u65b9\u6848<\/span>\uff08Z=1\u4e3a\u79ef\u6781\u6cbb\u7597\uff0cZ=0\u4e3a\u4fdd\u5b88\u6cbb\u7597\uff09<\/span>\uff0c\u8bb0Y\u4e3a\u6cbb\u7597\u4e24\u5e74\u540e\u751f\u6d3b\u8d28\u91cf\u662f\u5426\u6539\u5584<\/span>\uff08Y=1\u4e3a\u6539\u5584\uff0cY=0\u4e3a\u672a\u6539\u5584\uff09<\/span>\uff0cY\u662fZ\u7684\u6f5c\u5728\u7ed3\u679c\uff0c\u8bb0\u4e3aY(z)\u3002\u5b9e\u9645\u7814\u7a76\u5e38\u9047\u5230\u7684\u4e00\u4e2a\u95ee\u9898\u662f\uff0c\u60a3\u8005\u53ef\u80fd\u518d\u4e24\u5e74\u5185\u6b7b\u6389\uff0c\u5bfc\u81f4\u6536\u96c6\u4e0d\u5230\u7ed3\u5c40\u53d8\u91cf\u3002\u8bd5\u60f3\u4e00\u4e0b\uff0c\u5982\u679c\u4e00\u4e2a\u4eba\u6ca1\u6709\u6d3b\u7740\uff0c\u90a3\u8c08\u8bba\u4ed6\u7684\u751f\u6d3b\u8d28\u91cf\u8fd8\u6709\u610f\u4e49\u5417\uff1f\u6240\u4ee5\uff0c\u53ea\u6709\u5bf9\u5b58\u6d3b\u4e2a\u4f53\uff0c\u624d\u80fd\u5b9a\u4e49\u7ed3\u5c40\u53d8\u91cf\uff0c\u8fd9\u4e00\u95ee\u9898\u88ab\u53eb\u4f5c\u6b7b\u4ea1\u622a\u65ad\u95ee\u9898\u3002\u7528S\u8868\u793a\u4e2a\u4f53\u7684\u5b58\u6d3b\u72b6\u6001<\/span>\uff08S=1\u8868\u793a\u5b58\u6d3b\uff0cS=0\u8868\u793a\u6b7b\u4ea1\uff09<\/span>\uff0cS\u5176\u5b9e\u662fZ\u7684\u6f5c\u5728\u7ed3\u679c\uff0c\u8bb0\u4e3aS(z)\u3002\u6309\u7167S(z)\u53ef\u4ee5\u628a\u4eba\u7fa4\u5206\u4e3a\u56db\u5c42\uff1a<\/span><\/p>\n


<\/span><\/p>\n

a) S(0)=0, S(1)=0\u3002\u5373\u65e0\u8bba\u91c7\u53d6\u4f55\u79cd\u6cbb\u7597\u65b9\u6848\uff0c\u60a3\u8005\u90fd\u4f1a\u6b7b\u4ea1\u3002<\/span><\/section>\n
b) S(0)=1, S(1)=1\u3002\u5373\u65e0\u8bba\u91c7\u53d6\u4f55\u79cd\u6cbb\u7597\u65b9\u6848\uff0c\u60a3\u8005\u90fd\u4f1a\u5b58\u6d3b\u3002<\/span><\/section>\n
c) S(1)=1, S(0)=0\u3002\u5373\u5982\u679c\u63a5\u53d7\u79ef\u6781\u6cbb\u7597\u4f1a\u5b58\u6d3b\uff0c\u5982\u679c\u63a5\u53d7\u4fdd\u5b88\u6cbb\u7597\u4f1a\u6b7b\u4ea1\u3002<\/span><\/section>\n

d) S(0)=1, S(1)=0\u3002\u5373\u5982\u679c\u63a5\u53d7\u79ef\u6781\u6cbb\u7597\u4f1a\u6b7b\u4ea1\uff0c\u5982\u679c\u63a5\u53d7\u4fdd\u5b88\u6cbb\u7597\u4f1a\u5b58\u6d3b\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u5bf9\u4e8e\u7b2ca\u3001c\u3001d\u8fd9\u4e09\u7ec4\u4eba\u7fa4\uff0c\u81f3\u5c11\u6709\u4e00\u4e2a\u6f5c\u5728\u7ed3\u679cY(z)\u662f\u65e0\u5b9a\u4e49\u7684\uff0c\u6240\u4ee5\u5728\u8fd9\u4e09\u5c42\u4e2d\u6211\u4eec\u65e0\u6cd5\u7ed9\u51fa\u826f\u5b9a\u4e49\u7684\u56e0\u679c\u53c2\u6570\u3002\u53ea\u6709\u7b2cb\u7ec4\u4eba\u7fa4\u7684\u4e24\u4e2a\u6f5c\u5728\u7ed3\u679cY(z)\u90fd\u6709\u5b9a\u4e49\uff0c\u6211\u4eec\u53ef\u4ee5\u5728\u8fd9\u4e00\u5c42\u5185\u5b9a\u4e49\u5e78\u5b58\u8005\u5e73\u5747\u56e0\u679c\u4f5c\u7528\uff0c\u5373E[Y(1)-Y(0)|S(0)=1,S(1)=1]\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u4ec5\u4ec5\u901a\u8fc7\u89c2\u5bdf\u6570\u636e\u65e0\u6cd5\u5224\u65ad\u51fa\u4e00\u4e2a\u4e2a\u4f53\u5c5e\u4e8e\u54ea\u4e2a\u4e3b\u5c42\uff0c\u6240\u4ee5\u9700\u8981\u4e3a\u6240\u5b9a\u4e49\u7684\u56e0\u679c\u91cf\u627e\u5230\u5408\u7406\u7684\u89e3\u91ca\u624d\u6709\u5b9e\u9645\u610f\u4e49\u3002\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0c\u6b7b\u4ea1\u622a\u65ad\u7684\u95ee\u9898\u5728\u5176\u4ed6\u9886\u57df\u4e2d\u4e5f\u4f1a\u9047\u5230\u3002\u6bd4\u5982\u8981\u7814\u7a76\u7ed9\u5b66\u751f\u5956\u5b66\u91d1\u80fd\u5426\u4f1a\u63d0\u9ad8\u5b66\u751f\u6210\u7ee9\uff0c\u5b66\u751f\u6210\u7ee9\u53ea\u6709\u5728\u5176\u4e0d\u8f8d\u5b66\u65f6\u624d\u80fd\u5b9a\u4e49\uff1b\u8981\u7814\u7a76\u75ab\u82d7\u5bf9\u4e8e\u75c5\u6bd2\u8f7d\u91cf\u7684\u5f71\u54cd\uff0c\u75c5\u6bd2\u8f7d\u91cf\u53ea\u6709\u5f53\u4e00\u4e2a\u4eba\u611f\u67d3\u4e86\u624d\u80fd\u5b9a\u4e49\u3002<\/span><\/p>\n


<\/p>\n

 <\/span>
<\/section>\n

\n
\n
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\n
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<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

\u4e94\u3001\u968f\u673a\u5316\u771f\u7684\u662f\u91d1\u6807\u51c6\u5417\uff1f\u2014\u2014\u518d\u968f\u673a\u5316<\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

\u957f\u671f\u4ee5\u6765\uff0c\u968f\u673a\u5316\u4e00\u76f4\u88ab\u5f53\u6210\u662f\u8bc4\u4f30\u56e0\u679c\u4f5c\u7528\u7684\u91d1\u6807\u51c6\u3002\u5728\u968f\u673a\u5316\u8bd5\u9a8c\u4e2d\uff0c\u6bcf\u4e2a\u4e2a\u4f53\u88ab\u968f\u673a\u5206\u914d\u5230\u5404\u4e2a\u5904\u7406\u7ec4\uff0c\u56e0\u6b64\u7406\u8bba\u4e0a\u5404\u4e2a\u5904\u7406\u7ec4\u4e0b\u7684\u534f\u53d8\u91cfX\u7684\u5206\u5e03\u76f8\u4f3c\u3002\u4f7f\u7528\u5404\u4e2a\u5904\u7406\u7ec4\u4e0b\u7684\u89c2\u5bdf\u5230\u7684\u7ed3\u5c40\u5747\u503c\u5dee\u5f02\u80fd\u5bf9\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u8fdb\u884c\u65e0\u504f\u4f30\u8ba1\u3002\u7136\u800c\uff0c\u968f\u673a\u5b9e\u9a8c\u7684\u8fd9\u4e9b\u6027\u8d28\u53ea\u5bf9\u5927\u91cf\u91cd\u590d\u5b9e\u9a8c\u5e73\u5747\u800c\u8a00\u6210\u7acb\uff0c\u5728\u5b9e\u9645\u53ea\u505a\u4e00\u6b21\u5b9e\u9a8c\u7684\u60c5\u5f62\u4e0b\uff0c\u4e0d\u540c\u5904\u7406\u7ec4\u4e0b\u7684\u534f\u53d8\u91cf\u7684\u5206\u5e03\u53ef\u80fd\u6709\u663e\u8457\u5dee\u5f02\uff0c\u5747\u503c\u5dee\u5f02\u4f30\u8ba1\u91cf\u53ef\u80fd\u79bb\u56e0\u679c\u4f5c\u7528\u7684\u771f\u5b9e\u503c\u5f88\u8fdc\u3002\u4e3e\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\uff0c\u5047\u8bbe\u5728\u67d0\u6b21\u968f\u673a\u5316\u4e34\u5e8a\u8bd5\u9a8c\u4e2d\uff0c\u968f\u673a\u5206\u914d\u4e00\u4e9b\u4e2a\u4f53\u63a5\u53d7\u6cbb\u7597\u6216\u5bf9\u7167\uff0c\u4f46\u6cbb\u7597\u7ec4\u4e2d\u6070\u5de7\u5927\u90e8\u5206\u90fd\u662f\u8eab\u4f53\u865a\u5f31\u7684\u4e2a\u4f53\uff0c\u800c\u5bf9\u7167\u7ec4\u4e2d\u6070\u5de7\u5927\u90e8\u5206\u90fd\u662f\u8eab\u4f53\u5065\u58ee\u7684\u4e2a\u4f53\uff0c\u8fd9\u6837\uff0c\u4e24\u7ec4\u7684\u89c2\u6d4b\u7ed3\u5c40\u5747\u503c\u53d7\u5230\u60a3\u8005\u8eab\u4f53\u72b6\u51b5\u8fd9\u4e00\u4e0d\u5bb9\u5ffd\u89c6\u7684\u6df7\u6742\u56e0\u7d20\u7684\u5f71\u54cd\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u5982\u679c\u534f\u53d8\u91cf\u7684\u4e2a\u6570\u5f88\u591a\uff0c\u5355\u4e2a\u6216\u591a\u4e2a\u534f\u53d8\u91cf\u4e0d\u5e73\u8861\u7684\u73b0\u8c61\u5c31\u8d8a\u6709\u53ef\u80fd\u53d1\u751f\u3002\u5373\u4f7f\u589e\u5927\u6837\u672c\u91cf\uff0c\u5355\u6b21\u8bd5\u9a8c\u7684\u56e0\u679c\u4f5c\u7528\u4f30\u8ba1\u504f\u5dee\u95ee\u9898\u4e5f\u5f97\u4e0d\u5230\u89e3\u51b3\u3002\u8fd9\u662f\u56e0\u4e3a\uff0c\u867d\u7136\u968f\u7740\u6837\u672c\u91cfn\u7684\u589e\u5927\uff0c\u534f\u53d8\u91cf\u4ee5\u6839\u53f7n\u7684\u901f\u5ea6\u8d8b\u4e8e\u5e73\u8861\uff0c\u4f46\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u7684\u4f30\u8ba1\u91cf\u4e5f\u4ee5\u6839\u53f7n\u7684\u901f\u5ea6\u6536\u655b\uff0c\u8fd9\u5bfc\u81f4\u534f\u53d8\u91cf\u4e0d\u5e73\u8861\u9020\u6210\u7684\u504f\u5dee\u4e0e\u56e0\u679c\u4f5c\u7528\u7684\u91cf\u7ea7\u4ecd\u7136\u5904\u4e8e\u540c\u4e00\u5c3a\u5ea6\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u5f53\u9762\u4e34\u4e0d\u5408\u9002\u7684\u968f\u673a\u5206\u914d\u65f6\uff0cFisher\u66fe\u5efa\u8bae\u8fdb\u884c\u518d\u968f\u673a\u5316\u3002Morgan\u548cRubin\u9996\u6b21\u5bf9\u518d\u968f\u673a\u5316\u8fdb\u884c\u4e86\u6b63\u89c4\u7684\u6570\u5b66\u63cf\u8ff0[11]\uff0c\u5176\u57fa\u672c\u601d\u8def\u662f\uff1a\u9884\u5148\u6307\u5b9a\u67d0\u79cd\u8861\u91cf\u534f\u53d8\u91cf\u5728\u4e0d\u540c\u5904\u7406\u7ec4\u4e4b\u95f4\u5206\u5e03\u662f\u5426\u5e73\u8861\u7684\u51c6\u5219\uff0c\u4e0d\u91c7\u7eb3\u90a3\u4e9b\u534f\u53d8\u91cf\u4e0d\u5e73\u8861\u7684\u968f\u673a\u5206\u914d\uff0c\u800c\u662f\u4e00\u76f4\u8fdb\u884c\u968f\u673a\u5316\uff0c\u76f4\u5230\u83b7\u5f97\u534f\u53d8\u91cf\u5e73\u8861\u7684\u968f\u673a\u5206\u914d\u4e3a\u6b62\u3002Morgan\u548cRubin\u5efa\u8bae\u4f7f\u7528\u5904\u7406\u7ec4\u548c\u5bf9\u7167\u7ec4\u534f\u53d8\u91cf\u5747\u503c\u7684\u5e73\u65b9\u9a6c\u6c0f\u8ddd\u79bb\u4f5c\u4e3a\u51c6\u5219\uff0c\u53ea\u63a5\u53d7\u5e73\u65b9\u9a6c\u6c0f\u8ddd\u79bb\u5c0f\u4e8e\u67d0\u4e2a\u9608\u503c\u7684\u968f\u673a\u5206\u914d\u3002\u4ed6\u4eec\u8fd8\u6307\u51fa\uff0c\u901a\u8fc7\u518d\u968f\u673a\u5316\uff0c\u53ef\u4ee5\u5b9e\u73b0\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u4f30\u8ba1\u7684\u65b9\u5dee\u4e0b\u964d\u3002<\/span><\/p>\n


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\u518d\u968f\u673a\u5316\u5b9e\u9a8c\u7684\u7edf\u8ba1\u63a8\u65ad\u6bd4\u5b8c\u5168\u968f\u673a\u5316\u5b9e\u9a8c\u7684\u7edf\u8ba1\u63a8\u65ad\u66f4\u52a0\u590d\u6742\u3002\u6709\u4e00\u4e2a\u5904\u7406\u7ec4\u548c\u4e00\u4e2a\u5bf9\u7167\u7ec4\u5e76\u4f7f\u7528\u5e73\u65b9\u9a6c\u6c0f\u8ddd\u79bb\u51c6\u5219\u8fdb\u884c\u518d\u968f\u673a\u5316\u7684\u60c5\u5f62\u4e0b\uff0cMorgan\u548cRubin\u5efa\u8bae\u4f7f\u7528Fisher\u968f\u673a\u5316\u68c0\u9a8c\u8fdb\u884c\u7edf\u8ba1\u63a8\u65ad\u3002\u7531\u4e8e\u9650\u5236\u4e86\u5904\u7406\u7ec4\u548c\u5bf9\u7167\u7ec4\u4e4b\u95f4\u7684\u534f\u53d8\u91cf\u5206\u5e03\uff0c\u6240\u4ee5\u5904\u7406\u7ec4\u548c\u5bf9\u7167\u7ec4\u7684\u5e73\u5747\u7ed3\u5c40\u5dee\u5f02\u5e76\u4e0d\u518d\u670d\u4ece\u6b63\u6001\u5206\u5e03\uff0c\u800c\u662f\u670d\u4ece\u4e00\u4e2a\u6b63\u6001\u5206\u5e03\u548c\u53e6\u4e00\u4e2a\u622a\u65ad\u6b63\u6001\u5206\u5e03\u7684\u7ebf\u6027\u7ec4\u5408\u3002\u8fd1\u4e9b\u5e74\u6765\uff0c\u518d\u968f\u673a\u5316\u53d7\u5230\u4e86\u8d8a\u6765\u8d8a\u591a\u7684\u5173\u6ce8\uff0c\u4f8b\u5982\u534f\u53d8\u91cf\u5b58\u5728\u4e0d\u540c\u91cd\u8981\u68af\u5ea6\u65f6\u7684\u518d\u968f\u673a\u5316\u3001\u5e8f\u8d2f\u5b9e\u9a8c\u4e2d\u7684\u518d\u968f\u673a\u5316\u3002<\/span><\/p>\n


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\u53c2\u8003\u6587\u732e<\/span><\/strong><\/span><\/p>\n

[1] Neyman, J. S. (1923). On the application of probability theory to agricultural experiments. essay on principles. section 9. (Translated and edited by DM Dabrowska and TP Speed, statistical science (1990), 5, 465-480). Annals of Agricultural Sciences, 10, 1-51.<\/span><\/p>\n

[2] Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of educational Psychology, 66(5), 688.<\/span><\/p>\n

[3] Holland, P. W. (1986). Statistics and causal inference. Journal of the American statistical Association, 81(396), 945-960.<\/span><\/p>\n

[4] Rosenbaum, P. R., & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70(1), 41-55.<\/span><\/p>\n

[5] Angrist, J. D., Imbens, G. W., & Rubin, D. B. (1996). Identification of causal effects using instrumental variables. Journal of the American statistical Association, 91(434), 444-455.<\/span><\/p>\n

[6] Frangakis, C. E., & Rubin, D. B. (2002). Principal stratification in causal inference. Biometrics, 58(1), 21-29.<\/span><\/p>\n

[7] Morgan, K. L., & Rubin, D. B. (2012). Rerandomization to improve covariate balance in experiments. The Annals of Statistics, 40(2), 1263-1282.<\/span><\/p>\n


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\u56e0\u679c\u79d1\u5b66\u8bfb\u4e66\u4f1a\u7b2c\u4e09\u5b63\u542f\u52a8<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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\u6211\u4eec\u7279\u522b\u9080\u8bf7\u5230Donald B. Rubin\u6559\u6388\u4e8e10\u670822\u65e5\uff08\u5468\u4e94\uff0921:00\u5728\u8bfb\u4e66\u4f1a\u7b2c\u4e00\u671f\u505a\u62a5\u544a\uff0c\u6b22\u8fce\u611f\u5174\u8da3\u7684\u670b\u53cb\u62a5\u540d\u8bfb\u4e66\u4f1a\uff0c\u4e0eRubin\u4ea4\u6d41\u3002<\/span><\/p>\n


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Donald Rubin\uff1aEssential Concepts of causal inference<\/span><\/p>\n

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\u56e0\u679c\u63a8\u65ad\u5728\u89c2\u5bdf\u6027\u7814\u7a76\u4e2d\u7684\u5e94\u7528\uff1aDESIGN<\/span><\/p>\n

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