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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 Control variates ： ウィキペディア英語版 Control variates The control variates method is a variance reduction technique used in Monte Carlo methods. It exploits information about the errors in estimates of known quantities to reduce the error of an estimate of an unknown quantity.〔Glasserman, P. (2004). ''Monte Carlo Methods in Financial Engineering''. New York: Springer. ISBN 0-387-00451-3 (p. 185)〕 ==Underlying principle== Let the unknown parameter of interest be $\backslash mu$, and assume we have a statistic $m$ such that the expected value of ''m'' is μ: $\backslash mathbb\backslash left()=\backslash mu$, i.e. ''m'' is an unbiased estimator for μ. Suppose we calculate another statistic $t$ such that $\backslash mathbb\backslash left()=\backslash tau$ is a known value. Then :$m^\backslash star\; =\; m\; +\; c\backslash left(t-\backslash tau\backslash right)\; \backslash ,$ is also an unbiased estimator for $\backslash mu$ for any choice of the coefficient $c$. The variance of the resulting estimator $m^$ is :$\backslash textrm\backslash left(m^\backslash right)=\backslash textrm\backslash left(m\backslash right)\; +\; c^2\backslash ,\backslash textrm\backslash left(t\backslash right)\; +\; 2c\backslash ,\backslash textrm\backslash left(m,t\backslash right);$ It can be shown that choosing the optimal coefficient :$c^\backslash star\; =\; -\; \backslash frac;$ minimizes the variance of $m^$, and that with this choice, :$\backslash begin$ \textrm\left(m^\right) & =\textrm\left(m\right) - \frac\left(m,t\right)\right">)^2} \\ & = \left(1-\rho_^2\right)\textrm\left(m\right); \end where :$\backslash rho\_=\backslash textrm\backslash left(m,t\backslash right);\; \backslash ,$ is the correlation coefficient of ''m'' and ''t''. The greater the value of $\backslash vert\backslash rho\_\backslash vert$, the greater the variance reduction achieved. In the case that $\backslash textrm\backslash left(m,t\backslash right)$, $\backslash textrm\backslash left(t\backslash right)$, and/or $\backslash rho\_\backslash ;$ are unknown, they can be estimated across the Monte Carlo replicates. This is equivalent to solving a certain least squares system; therefore this technique is also known as regression sampling. 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「Control variates」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.