A new algorithm for spline smoothing based on smoothing a stochastic process
A new algorithm for spline smoothing based on smoothing a stochastic process
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DOI：
10.1137/0908004
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发表时间：
1987-01
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影响因子：
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通讯作者：
R. Kohn;C. Ansley
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文献类型：
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作者：
R. Kohn;C. Ansley
我们使用 Wahba 的随机模型，推导了一种新的有效算法，用于最优样条平滑，作为用噪声观察到的随机过程的条件期望（J. Royal Statist. Soc. Ser. B, 40 (1978), pp. 364–372）。条件期望是通过以状态空间形式表达过程并使用 Ansley 和 Kohn 中的过滤和平滑结果来计算的（Annals Statist., 11 (1985), pp.1286–1316）。我们展示了如何使用我们的算法来估计平滑参数以及如何获得未知函数及其导数的贝叶斯置信区间。将基于其他随机模型的算法与我们的算法进行了比较，并给出了 Reinsch（Numer. Math. 10 (1967), pp. 177–183）多项式样条算法的随机推导。
We derive a new efficient algorithm for optimal spline smoothing as the conditional expectation of a stochastic process observed with noise, using the stochastic model of Wahba (J. Royal Statist. Soc. Ser. B, 40 (1978), pp. 364–372). The conditional expectation is computed by expressing the process in state space form and using the filtering and smoothing results in Ansley and Kohn (Annals Statist., 11 (1985), pp.1286–1316). We show how to use our algorithms to estimate the smoothness parameter and how to obtain Bayesian confidence intervals for the unknown function and its derivatives. Algorithms based on other stochastic models are compared to ours, and a stochastic derivation is given for Reinsch’s (Numer. Math. 10 (1967), pp. 177–183) algorithm for polynomial splines.