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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 smoothing spline ： ウィキペディア英語版 smoothing spline The smoothing spline is a method of fitting a smooth curve to a set of noisy observations using a spline function. ==Definition== Let :$$ \sum_^n (Y_i - \hat\mu(x_i))^2 + \lambda \int_^ \hat\mu''(x)^2 \,dx. Remarks: * $\backslash lambda\; \backslash ge\; 0$ is a smoothing parameter, controlling the trade-off between fidelity to the data and roughness of the function estimate. * The integral is evaluated over the range of the $x\_i$. * As $\backslash lambda\backslash to\; 0$ (no smoothing), the smoothing spline converges to the interpolating spline. * As $\backslash lambda\backslash to\backslash infty$ (infinite smoothing), the roughness penalty becomes paramount and the estimate converges to a linear least squares estimate. * The roughness penalty based on the second derivative is the most common in modern statistics literature, although the method can easily be adapted to penalties based on other derivatives. * In early literature, with equally-spaced $x\_i$, second or third-order differences were used in the penalty, rather than derivatives. * When the sum-of-squares term is replaced by a log-likelihood, the resulting estimate is termed ''penalized likelihood''. The smoothing spline is the special case of penalized likelihood resulting from a Gaussian likelihood. 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「smoothing spline」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.