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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク scoring algorithm ： ウィキペディア英語版 scoring algorithm Scoring algorithm, also known as Fisher's scoring,〔(A fast scoring algorithm for maximum likelihood estimation in unbalanced mixed models with nested random effects )〕 is a form of Newton's method used in statistics to solve maximum likelihood equations numerically, named after Ronald Fisher. ==Sketch of Derivation== Let $Y\_1,\backslash ldots,Y\_n$ be random variables, independent and identically distributed with twice differentiable p.d.f. $f(y;\; \backslash theta)$, and we wish to calculate the maximum likelihood estimator (M.L.E.) $\backslash theta^$ * of $\backslash theta$. First, suppose we have a starting point for our algorithm $\backslash theta\_0$, and consider a Taylor expansion of the score function, $V(\backslash theta)$, about $\backslash theta\_0$: : $V(\backslash theta)\; \backslash approx\; V(\backslash theta\_0)\; -\; \backslash mathcal(\backslash theta\_0)(\backslash theta\; -\; \backslash theta\_0),\; \backslash ,$ where : $\backslash mathcal(\backslash theta\_0)\; =\; -\; \backslash sum\_^n\; \backslash left.\; \backslash nabla\; \backslash nabla^\; \backslash right|\_\; \backslash log\; f(Y\_i\; ;\; \backslash theta)$ is the observed information matrix at $\backslash theta\_0$. Now, setting $\backslash theta\; =\; \backslash theta^$ *, using that $V(\backslash theta^$ *) = 0 and rearranging gives us: : $\backslash theta^$ * \approx \theta_ + \mathcal^(\theta_)V(\theta_). \, We therefore use the algorithm : $\backslash theta\_\; =\; \backslash theta\_\; +\; \backslash mathcal^(\backslash theta\_)V(\backslash theta\_),\; \backslash ,$ and under certain regularity conditions, it can be shown that $\backslash theta\_m\; \backslash rightarrow\; \backslash theta^$ *. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「scoring algorithm」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.