{"id":2908,"date":"2020-08-22T11:00:00","date_gmt":"2020-08-22T02:00:00","guid":{"rendered":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/?p=2908"},"modified":"2020-08-19T10:03:52","modified_gmt":"2020-08-19T01:03:52","slug":"cwisd-mv","status":"publish","type":"post","link":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/cwisd-mv","title":{"rendered":"\u30a6\u30a3\u30b7\u30e3\u30fc\u30c8\u5206\u5e03\u306e\u671f\u5f85\u5024\u306e\u6c42\u3081\u65b9\u3010\u8a3c\u660e\u4ed8\u304d\u3067\u89e3\u8aac\u3011"},"content":{"rendered":"\n

\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u5927\u5b66\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2605\u2606\u2606\u2606<\/span><\/p>\n\n\n\n\n\n\n\n

\u3000\u3053\u306e\u8a18\u4e8b\u3067\u306f\u30a6\u30a3\u30b7\u30e3\u30fc\u30c8\u5206\u5e03\u306e\u671f\u5f85\u5024\u306e\u6c42\u3081\u65b9\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002\u5206\u6563\u306e\u6c42\u3081\u65b9\u306f\u5c11\u3005\u9762\u5012\uff08\u30d9\u30af\u30c8\u30eb\u5c55\u958b\u304a\u3088\u3073\u8981\u7d20\u3054\u3068\u306e\u30c1\u30a7\u30c3\u30af\u304c\u5fc5\u8981\uff09\u306a\u306e\u3067\u3001\u5206\u6563\u306b\u3064\u3044\u3066\u306f\u53d6\u308a\u6271\u308f\u306a\u3044\u3053\u3068\u306b\u3057\u307e\u3059\u3002\u307e\u305f\u671f\u5f85\u5024\u3001\u5206\u6563\u306f\u4e00\u822c\u7684\u306a\u30a6\u30a3\u30b7\u30e3\u30fc\u30c8\u5206\u5e03\uff08\\(n\\)\u304c\u975e\u6574\u6570\u306e\u5834\u5408\uff09\u306b\u306f\u4e0e\u3048\u3089\u308c\u3066\u3044\u306a\u3044\u306e\u3067\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3059\u3002\\(n\\)\u304c\u6574\u6570\u306e\u5834\u5408\u3001\u671f\u5f85\u5024\u306e\u5c0e\u51fa\u306f\u975e\u5e38\u306b\u5bb9\u6613\u306b\u3067\u304d\u307e\u3059\u3002\u30a6\u30a3\u30b7\u30e3\u30fc\u30c8\u5206\u5e03\u306e\u305d\u306e\u4ed6\u306e\u60c5\u5831\u306b\u3064\u3044\u3066\u306f\uff1c\u30a6\u30a3\u30b7\u30e3\u30fc\u30c8\u5206\u5e03\u306e\u57fa\u672c\u60c5\u5831\uff1e<\/a>\u3092\u304a\u8aad\u307f\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n\n

\n \n
\"\u30a6\u30a3\u30b7\u30e3\u30fc\u30c8\u5206\u5e03\"<\/div>\n
\n
\u30a6\u30a3\u30b7\u30e3\u30fc\u30c8\u5206\u5e03<\/div>\n
\u3000\u30a6\u30a3\u30b7\u30e3\u30fc\u30c8\u5206\u5e03\uff08wishart distribution\uff09\u306f\u3001\u9023\u7d9a\u578b\u306e\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u30a6\u30a3\u30b7\u30e3\u30fc\u30c8\u5206\u5e03\u306f\u30ab\u30a4\uff12\u4e57\u5206\u5e03\u3092\u591a\u6b21\u5143\u306b\u62e1\u5f35\u3057\u305f\u3082\u306e\u3068\u3057\u2026<\/div>\n <\/div>\n
<\/div>\n <\/a>\n <\/div>\n\n\n\n

\u30a6\u30a3\u30b7\u30e3\u30fc\u30c8\u5206\u5e03\u306e\u671f\u5f85\u5024\u30fb\u5206\u6563<\/h2>\n\n\n\n
\u671f\u5f85\u5024\u3068\u5206\u6563<\/strong><\/div>\n
\u30a6\u30a3\u30b7\u30e3\u30fc\u30c8\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\\(X\\sim W_{p}(n,\\ \\Sigma)\\)\u306e\u671f\u5f85\u5024\u30fb\u5206\u6563\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\n
\\begin{align}\n\\mathrm{E}[X]=n\\Sigma,\\ \\ \\ \\mathrm{Var}[X]=2n\\Sigma\\otimes \\Sigma\n\\end{align}<\/div>\n<\/div>\n\n\n\n

\u3000<\/p>\n\n\n\n

\u8a3c\u660e\uff08\u671f\u5f85\u5024\u306e\u307f\uff09<\/h3>\n\n\n\n

\u30a6\u30a3\u30b7\u30e3\u30fc\u30c8\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\\(X\\sim W_{p}(n,\\ \\Sigma)\\)\u306f\u3001\u4e92\u3044\u306b\u72ec\u7acb\u306a\u591a\u5909\u91cf\u6b63\u898f\u5206\u5e03\\(x_{i}\\sim N_{p}(0,\\ \\Sigma)\\)\uff08\\(i=1,\\cdots,n\\)\uff09\u3092\u7528\u3044\u3066\u3001

\\begin{align}X=\\sum_{i=1}^{n}x_{i}\\ {}^{T}\\!x_{i}\\sim W_{p}(n,\\ \\Sigma)\\end{align}<\/div>\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306b\u671f\u5f85\u5024\u3092\u3068\u308a\u307e\u3059\u3002\u3059\u308b\u3068
\\begin{align}
\\mathrm{E}[X] &= \\mathrm{E}\\left[ \\sum_{i=1}^{n}x_{i}\\ {}^{T}\\!x_{i} \\right] \\\\
&= \\sum_{i=1}^{n}\\mathrm{E}\\left[ x_{i}\\ {}^{T}\\!x_{i} \\right] \\\\
&= n\\frac{1}{n}\\sum_{i=1}^{n} \\mathrm{E}\\left[ (x_{i}-\\mathrm{E}[x_{i}])\\ {}^{T}\\!(x_{i}-\\mathrm{E}[x_{i}]) \\right] \\\\
&= n\\Sigma
\\end{align}<\/div>\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n

\u25a1<\/p>\n","protected":false},"excerpt":{"rendered":"

\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u5927\u5b66\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2605\u2606\u2606\u2606 \u3000\u3053\u306e\u8a18\u4e8b\u3067\u306f\u30a6\u30a3\u30b7\u30e3\u30fc\u30c8\u5206\u5e03\u306e\u671f\u5f85\u5024\u306e\u6c42\u3081\u65b9\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002\u5206\u6563\u306e\u6c42\u3081\u65b9\u306f\u5c11\u3005\u9762\u5012\uff08\u30d9\u30af\u30c8\u30eb\u5c55\u958b\u304a\u3088 … <\/p>\n","protected":false},"author":1,"featured_media":196,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[72],"tags":[122,73],"jetpack_featured_media_url":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/05\/fe5298b70d9972a91424adc0358d5ef6_t.jpeg","_links":{"self":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/2908"}],"collection":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/comments?post=2908"}],"version-history":[{"count":3,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/2908\/revisions"}],"predecessor-version":[{"id":2911,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/2908\/revisions\/2911"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media\/196"}],"wp:attachment":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media?parent=2908"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/categories?post=2908"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/tags?post=2908"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}