{"id":298,"date":"2023-08-02T22:47:33","date_gmt":"2023-08-02T22:47:33","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%8f%82%e6%95%b0%e4%bc%b0%e8%ae%a1\/"},"modified":"2023-08-02T22:47:33","modified_gmt":"2023-08-02T22:47:33","slug":"%e5%8f%82%e6%95%b0%e4%bc%b0%e8%ae%a1","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%8f%82%e6%95%b0%e4%bc%b0%e8%ae%a1\/","title":{"rendered":"\u53c2\u6570\u4f30\u8ba1"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u53c2\u6570\u4f30\u8ba1\u662f\u4ec0\u4e48\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u5728\u7edf\u8ba1\u4e2d\u4f30\u8ba1\u53c2\u6570\u3001\u4e0d\u540c\u7c7b\u578b\u7684\u4f30\u8ba1\u4ee5\u53ca\u53c2\u6570\u4f30\u8ba1\u7684\u793a\u4f8b\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-estimacion-de-parametros\"><\/span>\u4ec0\u4e48\u662f\u53c2\u6570\u4f30\u8ba1\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u53c2\u6570\u4f30\u8ba1<\/strong>\u662f\u4e00\u79cd\u4ece\u6837\u672c\u4e2d\u4f30\u8ba1\u603b\u4f53\u53c2\u6570\u503c\u7684\u7edf\u8ba1\u65b9\u6cd5\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u53c2\u6570\u4f30\u8ba1\u7528\u4e8e\u901a\u8fc7\u5bf9\u6570\u636e\u6837\u672c\u6267\u884c\u8ba1\u7b97\u6765\u8fd1\u4f3c\u603b\u4f53\u53c2\u6570\u3002<\/p>\n<p>\u4e00\u822c\u6765\u8bf4\uff0c\u7fa4\u4f53\u7684\u53c2\u6570\u662f\u672a\u77e5\u7684\uff0c\u800c\u4e14\u7fa4\u4f53\u901a\u5e38\u592a\u5927\u800c\u65e0\u6cd5\u7814\u7a76\u5176\u6240\u6709\u4e2a\u4f53\u3002\u56e0\u6b64\uff0c\u62bd\u53d6\u603b\u4f53\u6837\u672c\uff0c\u5bf9\u8be5\u6837\u672c\u8fdb\u884c\u7edf\u8ba1\u5206\u6790\uff0c\u6700\u540e\u4ece\u6574\u4e2a\u603b\u4f53\u4e2d\u63a8\u5bfc\u51fa\u83b7\u5f97\u7684\u7ed3\u679c\u3002\u56e0\u6b64\uff0c\u7edf\u8ba1\u53c2\u6570\u7684\u4f30\u8ba1\u4f7f\u6211\u4eec\u80fd\u591f\u5927\u81f4\u4e86\u89e3\u603b\u4f53\u53c2\u6570\u7684\u503c\u3002<\/p>\n<p>\u5728\u4f30\u8ba1\u53c2\u6570\u65f6\uff0c\u603b\u662f\u5b58\u5728\u8bef\u5dee\u8303\u56f4\u3002\u7531\u4e8e\u603b\u4f53\u53c2\u6570\u7684\u771f\u5b9e\u503c\u901a\u5e38\u662f\u672a\u77e5\u7684\uff0c\u5728\u4f30\u8ba1\u53c2\u6570\u65f6\uff0c\u4f1a\u8fdb\u884c\u8fd1\u4f3c\uff0c\u56e0\u6b64\u53ef\u80fd\u4f1a\u51fa\u73b0\u771f\u5b9e\u503c\u4e0e\u8fd1\u4f3c\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-estimaciones-de-parametros\"><\/span>\u53c2\u6570\u4f30\u8ba1\u7684\u7c7b\u578b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u6709\u4e24\u79cd<strong>\u7c7b\u578b\u7684\u53c2\u6570\u4f30\u8ba1<\/strong>\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u5177\u4f53\u53c2\u6570\u4f30\u8ba1<\/strong>\uff1a\u6d89\u53ca\u5c06\u603b\u4f53\u53c2\u6570\u7684\u503c\u4f30\u8ba1\u4e3a\u7279\u5b9a\u503c\u3002\u901a\u5e38\uff0c\u6837\u672c\u53c2\u6570\u503c\u7528\u4f5c\u603b\u4f53\u53c2\u6570\u7684\u4f30\u8ba1\u3002<\/span><\/li>\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u6309\u533a\u95f4\u4f30\u8ba1\u53c2\u6570<\/strong>\uff1a\u5b83\u57fa\u4e8e\u5bf9\u5177\u6709\u533a\u95f4\u7684\u603b\u4f53\u53c2\u6570\u7684\u4f30\u8ba1\u3002\u56e0\u6b64\uff0c\u5b83\u4e0d\u662f\u5c06\u603b\u4f53\u53c2\u6570\u8fd1\u4f3c\u4e3a\u5355\u4e2a\u503c\uff0c\u800c\u662f\u8fd1\u4f3c\u4e00\u4e2a\u503c\u8303\u56f4\u3002<\/span><\/li>\n<\/ul>\n<p>\u70b9\u4f30\u8ba1\u6bd4\u533a\u95f4\u4f30\u8ba1\u66f4\u7cbe\u786e\uff0c\u56e0\u4e3a\u5b83\u5c06\u8fd1\u4f3c\u503c\u51cf\u5c11\u4e3a\u5355\u4e2a\u503c\u3002\u7136\u800c\uff0c\u533a\u95f4\u4f30\u8ba1\u66f4\u53ef\u9760\uff0c\u56e0\u4e3a\u53c2\u6570\u7684\u771f\u5b9e\u503c\u6bd4\u4f7f\u7528\u70b9\u4f30\u8ba1\u786e\u5b9a\u5176\u7cbe\u786e\u503c\u66f4\u6709\u53ef\u80fd\u4f4d\u4e8e\u533a\u95f4\u5185\u3002 <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u70b9\u4f30\u8ba11\/\">\u70b9\u4f30\u8ba1\u793a\u4f8b<\/a><br \/><span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u533a\u95f4\u4f30\u8ba1\/\">\u533a\u95f4\u4f30\u8ba1\u793a\u4f8b<\/a><\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"estimacion-puntual\"><\/span> \u70b9\u4f30\u8ba1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u70b9\u4f30\u8ba1<\/strong>\u6d89\u53ca\u4ece\u6837\u672c\u6570\u636e\u4f30\u8ba1\u603b\u4f53\u53c2\u6570\u7684\u7cbe\u786e\u503c\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u70b9\u4f30\u8ba1\u4f7f\u7528\u53c2\u6570\u7684\u6837\u672c\u503c\u4f5c\u4e3a\u53c2\u8003\u6765\u63d0\u4f9b\u603b\u4f53\u53c2\u6570\u7684\u5177\u4f53\u503c\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u8981\u786e\u5b9a 1,000 \u4eba\u7684\u603b\u4f53\u5e73\u5747\u503c\uff0c\u6211\u4eec\u53ef\u4ee5\u8fdb\u884c\u70b9\u4f30\u8ba1\u5e76\u8ba1\u7b97 50 \u4eba\u6837\u672c\u7684\u5e73\u5747\u503c\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u6837\u672c\u5747\u503c\u4f5c\u4e3a\u603b\u4f53\u5747\u503c\u7684\u70b9\u4f30\u8ba1\u3002<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u4f30\u8ba1\u91cf<\/strong>\u662f\u7528\u4e8e\u4f30\u8ba1\u603b\u4f53\u53c2\u6570\u503c\u7684\u6837\u672c\u7edf\u8ba1\u91cf\u3002\u56e0\u6b64\uff0c\u6837\u672c\u53c2\u6570\u7684\u503c\u88ab\u89c6\u4e3a\u603b\u4f53\u53c2\u6570\u503c\u7684\u4f30\u8ba1\u3002 <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u4f30\u8ba1\u5668\/\">\u4f18\u79c0\u4f30\u7b97\u5668\u7684\u7279\u5f81<\/a><\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"estimacion-por-intervalos\"><\/span>\u4f30\u8ba1\u533a\u95f4<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u533a\u95f4\u4f30\u8ba1<\/strong>\u6d89\u53ca\u4f7f\u7528\u533a\u95f4\u4f30\u8ba1\u603b\u4f53\u53c2\u6570\u7684\u503c\u3002\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\u533a\u95f4\u4f30\u8ba1\u6d89\u53ca\u8ba1\u7b97\u53c2\u6570\u503c\u6700\u6709\u53ef\u80fd\u4ee5\u4e00\u5b9a\u7f6e\u4fe1\u5ea6\u4e0b\u964d\u7684\u533a\u95f4\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u5982\u679c\u5728\u533a\u95f4\u4f30\u8ba1\u4e2d\uff0c\u6211\u4eec\u5f97\u51fa\u7ed3\u8bba\uff0c\u603b\u4f53\u5e73\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\u4e3a (3.7)\uff0c\u7f6e\u4fe1\u6c34\u5e73\u4e3a 95%\uff0c\u8fd9\u610f\u5473\u7740\u6240\u7814\u7a76\u603b\u4f53\u7684\u5e73\u5747\u503c\u5c06\u5728 3 \u5230 7 \u4e4b\u95f4\uff0c\u6982\u7387\u4e3a 95 %\u3002<\/p>\n<p>\u63d0\u4f9b\u533a\u95f4\u4f30\u8ba1\u7684\u533a\u95f4\u79f0\u4e3a\u7f6e\u4fe1\u533a\u95f4\u3002\u56e0\u6b64\uff0c<strong>\u7f6e\u4fe1\u533a\u95f4<\/strong>\u662f\u4e00\u4e2a\u533a\u95f4\uff0c\u5b83\u7ed9\u51fa\u4e86\u603b\u4f53\u53c2\u6570\u503c\u4e4b\u95f4\u7684\u503c\u7684\u4f30\u8ba1\u503c\uff08\u5177\u6709\u8bef\u5dee\u5e45\u5ea6\uff09\u3002\u7b80\u800c\u8a00\u4e4b\uff0c\u7f6e\u4fe1\u533a\u95f4\u662f\u533a\u95f4\u4f30\u8ba1\u5f97\u5230\u7684\u7ed3\u679c\u3002\u8981\u8ba1\u7b97\u533a\u95f4\u4f30\u8ba1\u7684\u7f6e\u4fe1\u533a\u95f4\uff0c\u5fc5\u987b\u5e94\u7528\u76f8\u5e94\u7684\u516c\u5f0f\uff1a <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u7f6e\u4fe1\u533a\u95f4\/\">\u7f6e\u4fe1\u533a\u95f4\u516c\u5f0f<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-estimacion-de-un-parametro\"><\/span>\u4f30\u8ba1\u53c2\u6570\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u53c2\u6570\u4f30\u8ba1\u7684\u5b9a\u4e49\u4ee5\u53ca\u53c2\u6570\u4f30\u8ba1\u7684\u4e0d\u540c\u7c7b\u578b\uff0c\u6211\u4eec\u5c06\u770b\u5230\u5982\u4f55\u4f30\u8ba1\u603b\u4f53\u53c2\u6570\u7684\u793a\u4f8b\u3002<\/p>\n<ul>\n<li>\u5728\u5e02\u573a\u8c03\u67e5\u4e2d\uff0c\u6211\u4eec\u60f3\u8981\u786e\u5b9a\u8033\u673a\u7684\u5e73\u5747\u4ef7\u683c\u3002\u4e0d\u8fc7\u578b\u53f7\u592a\u591a\uff0c\u4e0d\u53ef\u80fd\u7814\u7a76\u5168\u90e8\u7684\u4ef7\u683c\uff0c\u6240\u4ee5\u51b3\u5b9a\u4ece\u53bb\u5e74\u8033\u673a\u9500\u91cf\u6700\u591a\u7684\u4e94\u4e2a\u54c1\u724c\u4e2d\u8fdb\u884c\u62bd\u6837\uff08\u6570\u636e\u5982\u4e0b\uff09\u3002\u5076\u5c14\u5e76\u95f4\u9694\u5730\u4f30\u8ba1\u4eba\u53e3\u7684\u5e73\u5747\u4ef7\u683c\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"> 25 8 14 19 12<\/p>\n<p>\u8981\u51c6\u786e\u4f30\u8ba1\u603b\u4f53\u5e73\u5747\u503c\uff0c\u53ea\u9700\u8ba1\u7b97\u6837\u672c\u6570\u636e\u7684\u5e73\u5747\u503c\u5373\u53ef\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5e94\u7528\u7b97\u672f\u516c\u5f0f\u5747\u503c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-10464a7b322e8a792aa6555d2a7ea5b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x}=\\cfrac{25+8+14+19+12}{5}=15,6\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"260\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u4f46\u662f\uff0c\u6211\u4eec\u5c06\u6309\u7f6e\u4fe1\u5ea6\u4e3a 95% \u7684\u533a\u95f4\u8fdb\u884c\u4f30\u8ba1\uff0c\u56e0\u4e3a\u8fd9\u662f\u6700\u5e38\u89c1\u7684\u7f6e\u4fe1\u5ea6\u3002\u56e0\u6b64\uff0c\u8981\u8fdb\u884c\u533a\u95f4\u4f30\u8ba1\uff0c\u6709\u5fc5\u8981\u5e94\u7528<a href=\"https:\/\/statorials.org\/cn\/\u5e73\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\/\">\u5e73\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\u516c\u5f0f<\/a>\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-68cadfed993f46df534da0b30f15e7dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(7,43 \\ , \\ 23,77 )\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"error-de-estimacion\"><\/span>\u4f30\u8ba1\u8bef\u5dee<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\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<p>\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u77e5\u9053\u603b\u4f53\u53c2\u6570\u7684\u503c\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u8ba1\u7b97\u4f30\u8ba1\u8bef\u5dee\uff0c\u5176\u5b9a\u4e49\u4e3a\u53c2\u6570\u7684\u4f30\u8ba1\u503c\u4e0e\u771f\u5b9e\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-256c75a75baeb32bb5b868fcbd86d44b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e=\\widehat{\\theta}-\\theta\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"71\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u91d1\u5b50<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0bd3dc61f3221d4a03d802a8cd668c9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{\\theta}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u4f30\u8ba1\u503c\uff0c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7b2034939b850e3311120fca462ab64e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\theta\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u53c2\u6570\u7684\u5b9e\u9645\u503c\u3002<\/p>\n<p>\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<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-feb09d7331847ec133669821057453f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle ECM=\\cfrac{1}{n}\\sum_{i=1}^n \\left(\\widehat{\\theta}-\\theta \\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"182\" style=\"vertical-align: 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href=\"https:\/\/statorials.org\/cn\/\u5047\u8bbe\u5bf9\u6bd4\/\">\u4ec0\u4e48\u662f\u5047\u8bbe\u68c0\u9a8c\uff1f<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u53c2\u6570\u4f30\u8ba1\u662f\u4ec0\u4e48\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u5728\u7edf\u8ba1\u4e2d\u4f30\u8ba1\u53c2\u6570\u3001\u4e0d\u540c\u7c7b\u578b\u7684\u4f30\u8ba1\u4ee5\u53ca\u53c2\u6570\u4f30\u8ba1\u7684\u793a\u4f8b\u3002 \u4ec0 [&hellip;]<\/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-298","post","type-post","status-publish","format-standard","hentry","category-14"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 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