{"id":80,"date":"2023-08-05T17:04:07","date_gmt":"2023-08-05T17:04:07","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e9%80%80%e5%8d%8f%e6%96%b9%e5%b7%ae%e7%9f%a9%e9%98%b5\/"},"modified":"2023-08-05T17:04:07","modified_gmt":"2023-08-05T17:04:07","slug":"%e9%80%80%e5%8d%8f%e6%96%b9%e5%b7%ae%e7%9f%a9%e9%98%b5","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e9%80%80%e5%8d%8f%e6%96%b9%e5%b7%ae%e7%9f%a9%e9%98%b5\/","title":{"rendered":"\u534f\u65b9\u5dee\u77e9\u9635"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4ec0\u4e48\u662f\u534f\u65b9\u5dee\u77e9\u9635\u4ee5\u53ca\u5b83\u7684\u516c\u5f0f\u662f\u4ec0\u4e48\u3002\u60a8\u5c06\u901a\u8fc7\u5177\u4f53\u793a\u4f8b\u4e86\u89e3\u5982\u4f55\u521b\u5efa\u534f\u65b9\u5dee\u77e9\u9635\u4ee5\u53ca\u534f\u65b9\u5dee\u77e9\u9635\u7684\u5c5e\u6027\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-matriz-de-covarianza\"><\/span>\u4ec0\u4e48\u662f\u534f\u65b9\u5dee\u77e9\u9635\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u534f\u65b9\u5dee\u77e9\u9635<\/strong>\u662f\u4e00\u4e2a\u65b9\u9635\uff0c\u5176\u5143\u7d20\u662f\u6240\u7814\u7a76\u53d8\u91cf\u7684\u65b9\u5dee\u548c\u534f\u65b9\u5dee\u3002\u56e0\u6b64\uff0c\u534f\u65b9\u5dee\u77e9\u9635\u4e3b\u5bf9\u89d2\u7ebf\u7684\u5143\u7d20\u662f\u6bcf\u4e2a\u53d8\u91cf\u7684\u65b9\u5dee\uff0c\u5176\u4f59\u5143\u7d20\u662f\u53d8\u91cf\u4e4b\u95f4\u7684\u534f\u65b9\u5dee\u3002<\/p>\n<p>\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u534f\u65b9\u5dee\u77e9\u9635\u7528\u4e8e\u5206\u6790\u4e24\u4e2a\u6216\u591a\u4e2a\u968f\u673a\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u534f\u65b9\u5dee\u77e9\u9635\u975e\u5e38\u6709\u7528\uff0c\u56e0\u4e3a\u5b83\u53ef\u4ee5\u8ba9\u60a8\u5feb\u901f\u89e3\u91ca\u8bb8\u591a\u53d8\u91cf\u4e4b\u95f4\u7684\u76f8\u5173\u6027\uff0c\u56e0\u4e3a\u60a8\u53ef\u4ee5\u540c\u65f6\u770b\u5230\u53d8\u91cf\u7684\u6240\u6709\u534f\u65b9\u5dee\u7684\u503c\u3002<\/p>\n<p>\u534f\u65b9\u5dee\u77e9\u9635\u7684\u7b26\u53f7\u662f\u5927\u5199\u5e0c\u814a\u5b57\u6bcd\u897f\u683c\u739b\uff08\u03a3\uff09\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-matriz-de-covarianza\"><\/span>\u5982\u4f55\u8ba1\u7b97\u534f\u65b9\u5dee\u77e9\u9635<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8981<strong>\u8ba1\u7b97\u591a\u4e2a\u7edf\u8ba1\u53d8\u91cf\u7684\u534f\u65b9\u5dee\u77e9\u9635<\/strong>\uff0c\u5fc5\u987b\u6267\u884c\u4ee5\u4e0b\u6b65\u9aa4\uff1a<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:14px\"><span style=\"color:#101010;font-weight: normal;\">\u8ba1\u7b97\u6240\u6709\u53d8\u91cf\u7684\u65b9\u5dee\u3002<\/span><\/li>\n<li style=\"margin-bottom:14px\"><span style=\"color:#101010;font-weight: normal;\">\u8ba1\u7b97\u6bcf\u5bf9\u53d8\u91cf\u7684\u534f\u65b9\u5dee\u3002<\/span><\/li>\n<li style=\"margin-bottom:8px\"><span style=\"color:#101010;font-weight: normal;\">\u5f62\u6210\u534f\u65b9\u5dee\u77e9\u9635\uff1a<\/span><\/li>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:8px\"><span style=\"color:#101010;font-weight: normal;\">\u53d8\u91cf<em>i<\/em>\u7684\u65b9\u5dee\u5fc5\u987b\u653e\u7f6e\u5728\u77e9\u9635\u7684\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\uff0c\u66f4\u51c6\u786e\u5730\u8bf4\u662f\u653e\u7f6e\u5728\u4f4d\u7f6e<em>i,i<\/em>\u4e0a\u3002<\/span><\/li>\n<li style=\"margin-bottom:8px\"><span style=\"color:#101010;font-weight: normal;\">\u53d8\u91cf<em>i<\/em>\u548c<em>j<\/em>\u4e4b\u95f4\u7684\u534f\u65b9\u5dee\u5fc5\u987b\u653e\u5728\u77e9\u9635\u7684<em>i,j<\/em>\u4f4d\u7f6e\u3002<\/span><\/li>\n<\/ul>\n<\/ol>\n<p>\u56e0\u6b64<strong>\u534f\u65b9\u5dee\u77e9\u9635\u7684\u516c\u5f0f<\/strong>\u5982\u4e0b\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/matrice-de-covariance.png\" alt=\"\u534f\u65b9\u5dee\u77e9\u9635\" class=\"wp-image-1714\" width=\"602\" height=\"219\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-matriz-de-covarianza\"><\/span>\u534f\u65b9\u5dee\u77e9\u9635\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u770b\u5230\u534f\u65b9\u5dee\u77e9\u9635\u7684\u5b9a\u4e49\u540e\uff0c\u4e0b\u9762\u662f\u4e00\u4e2a\u5206\u6b65\u7ec3\u4e60\uff0c\u4ee5\u4fbf\u60a8\u53ef\u4ee5\u4e86\u89e3\u8fd9\u79cd\u7c7b\u578b\u7684\u77e9\u9635\u662f\u5982\u4f55\u5236\u4f5c\u7684\u3002<\/p>\n<p>\u8ba1\u7b97\u53d8\u91cfX\u3001Y\u548cZ\u7684\u534f\u65b9\u5dee\u77e9\u9635\uff0c\u5176\u503c\u4e3a\uff1a<\/p>\n<ul>\n<li> X\uff1a4\u30017\u300112\u30015\u30017<\/li>\n<li>\u8fd8\u6709\uff1a9\u300115\u300119\u30016\u30018<\/li>\n<li> Z\uff1a7\u30012\u30014\u30016\u30013<\/li>\n<\/ul>\n<p>\u6211\u4eec\u9700\u8981\u505a\u7684\u7b2c\u4e00\u4ef6\u4e8b\u662f\u786e\u5b9a\u6240\u6709\u53d8\u91cf\u7684\u65b9\u5dee\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-246675afb851649ad3289cc9fdd86de8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=7,6\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -5px;\"><\/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-04c40f4402759ea0ba6b1507f0865564_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(Y)=23,44\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"127\" style=\"vertical-align: -5px;\"><\/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-3b9aa0b6c1af85b98c41d6e91c2d42ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(Z)=3,44\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"118\" style=\"vertical-align: -5px;\"><\/p>\n<\/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\/\u65b9\u5dee\/\">\u95f4\u9699\u8ba1\u7b97\u5668<\/a><\/div>\n<p>\u5176\u6b21\uff0c\u6211\u4eec\u627e\u5230\u6bcf\u5bf9\u53d8\u91cf\u4e4b\u95f4\u7684\u534f\u65b9\u5dee\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-997ada9147a8e29f8e808795aebb7c90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Cov(X,Y)=11,2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"140\" style=\"vertical-align: -5px;\"><\/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-e7c4b2aa6cd24dabf9c4538030f30b1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Cov(X,Z)=-2,6\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"145\" style=\"vertical-align: -5px;\"><\/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-3f9c1dab7f4691d9a35e56e3e166d919_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Cov(Y,Z)=-4,36\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"150\" style=\"vertical-align: -5px;\"><\/p>\n<\/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\/\u534f\u65b9\u5dee\/\">\u534f\u65b9\u5dee\u8ba1\u7b97\u5668<\/a><\/div>\n<p>\u4e00\u65e6\u6211\u4eec\u8ba1\u7b97\u4e86\u6240\u6709\u65b9\u5dee\u548c\u534f\u65b9\u5dee\uff0c\u5269\u4e0b\u7684\u5c31\u662f\u5236\u4f5c\u534f\u65b9\u5dee\u77e9\u9635\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u65b9\u5dee\u503c\u653e\u5728\u77e9\u9635\u7684\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\uff0c\u5c06\u534f\u65b9\u5dee\u503c\u653e\u5728\u5176\u76f8\u5e94\u7684\u4f4d\u7f6e\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-3a423b40ad6d25b57327b1f3dccd5df4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Sigma=\\begin{pmatrix}Var(X)&amp;Cov(X,Y)&amp;Cov(X,Z)\\\\[1.5ex]Cov(Y,X)&amp;Var(Y)&amp;Cov(Y,Z)\\\\[1.5ex]Cov(Z,X)&amp;Cov(Z,Y)&amp;Var(Z)\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"342\" style=\"vertical-align: 0px;\"><\/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-d90c58cc3c8ecef6a85c88196e1dd08d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Sigma=\\begin{pmatrix}7,6&amp;11,2&amp;-2,6\\\\[1.5ex]11,2&amp;23,44&amp;-4,36\\\\[1.5ex]-2,6&amp;-4,36&amp;3,44\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"231\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6b63\u5982\u60a8\u6240\u770b\u5230\u7684\uff0c\u901a\u8fc7\u5728\u77e9\u9635\u4e2d\u8868\u793a\u65b9\u5dee\u548c\u534f\u65b9\u5dee\uff0c\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u89e3\u91ca\u53d8\u91cf\u3002\u79bb\u5dee\u6700\u5927\u7684\u53d8\u91cf\u662f Y (23.44)\uff0c\u53e6\u4e00\u65b9\u9762\uff0c\u53d8\u91cf X \u548c Y \u5177\u6709\u6b63\u76f8\u5173\u5173\u7cfb\uff0c\u800c\u53d8\u91cf X \u548c Z\uff08\u56e0\u6b64 Y \u548c Z\uff09\u5177\u6709\u53cd\u76f8\u5173\u5173\u7cfb\u3002<\/p>\n<p>\u8bf7\u6ce8\u610f\uff0c\u534f\u65b9\u5dee\u77e9\u9635\u59cb\u7ec8\u662f\u5bf9\u79f0\u7684\uff0c\u56e0\u4e3a\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u534f\u65b9\u5dee\u4e0d\u53d6\u51b3\u4e8e\u53d8\u91cf\u7684\u987a\u5e8f\u3002\u4f8b\u5982\uff0c<\/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-eba027bd1998d2c1dbe59f1b512ab953_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Cov(X,Y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u7b49\u4e8e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-def16a63c06994394f83cdc040bea555_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Cov(Y,X).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6b64\u5916\uff0c\u534f\u65b9\u5dee\u77e9\u9635\u59cb\u7ec8\u662f\u65b9\u9635\uff0c\u5176\u7ef4\u5ea6\u5c06\u7b49\u4e8e\u53d8\u91cf\u7684\u6570\u91cf\u3002\u5728\u672c\u4f8b\u4e2d\uff0c\u6211\u4eec\u6709\u4e09\u4e2a\u53d8\u91cf\uff0c\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u5b83\u662f 3&#215;3 \u77e9\u9635\uff0c\u4f46\u5982\u679c\u6211\u4eec\u53ea\u6709\u4e24\u4e2a\u53d8\u91cf\uff0c\u534f\u65b9\u5dee\u77e9\u9635\u5c06\u4e3a 2&#215;2\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-matriz-de-covarianza\"><\/span>\u534f\u65b9\u5dee\u77e9\u9635\u7684\u5c5e\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u534f\u65b9\u5dee\u77e9\u9635\u5177\u6709\u4ee5\u4e0b\u7279\u70b9\uff1a<\/p>\n<ul>\n<li>\u534f\u65b9\u5dee\u77e9\u9635\u662f\u53d8\u91cf\u6570\u91cf\u9636\u7684\u65b9\u9635\u3002<\/li>\n<li>\u534f\u65b9\u5dee\u77e9\u9635\u662f\u5bf9\u79f0\u7684\uff0c\u8fd9\u610f\u5473\u7740\u77e9\u9635\u7684\u4e3b\u5bf9\u89d2\u7ebf\u662f\u5bf9\u79f0\u8f74\u3002<\/li>\n<li>\u534f\u65b9\u5dee\u77e9\u9635\u59cb\u7ec8\u662f\u534a\u6b63\u5b9a\u7684\u3002<\/li>\n<li>\u534f\u65b9\u5dee\u77e9\u9635\u7684\u884c\u5217\u5f0f\u7b49\u4e8e\u6216\u5927\u4e8e\u96f6\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4ec0\u4e48\u662f\u534f\u65b9\u5dee\u77e9\u9635\u4ee5\u53ca\u5b83\u7684\u516c\u5f0f\u662f\u4ec0\u4e48\u3002\u60a8\u5c06\u901a\u8fc7\u5177\u4f53\u793a\u4f8b\u4e86\u89e3\u5982\u4f55\u521b\u5efa\u534f\u65b9\u5dee\u77e9\u9635\u4ee5\u53ca\u534f\u65b9\u5dee\u77e9\u9635\u7684\u5c5e\u6027\u3002 \u4ec0\u4e48 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