Improper Priors, Spline Smoothing and the Problem of Guarding Against Model Errors in Regression
Improper Priors, Spline Smoothing and the Problem of Guarding Against Model Errors in Regression
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DOI：
10.1111/j.2517-6161.1978.tb01050.x
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发表时间：
1978-07
期刊：
影响因子：
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通讯作者：
G. Wahba
中科院分区：
文献类型：
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作者：
G. Wahba
摘要样条和广义样条平滑被证明是等价于贝叶斯估计与部分不适当的前。这一结果支持了这样的想法，即样条平滑是回归问题的自然解决方案，当一个给定的一组回归函数，但也要对冲的可能性，真正的模型是不完全在给定的回归函数的跨度。真实模型与回归函数跨度的偏差的自然度量以自然的方式来自样条理论。可以从数据中估计该度量的适当值，并将其用于约束估计模型以具有估计偏差。文中还讨论了一些收敛性结果和计算技巧。
SUMMARY Spline and generalized spline smoothing is shown to be equivalent to Bayesian estimation with a partially improper prior. This result supports the idea that spline smoothing is a natural solution to the regression problem when one is given a set of regression functions but one also wants to hedge against the possibility that the true model is not exactly in the span of the given regression functions. A natural measure of the deviation of the true model from the span of the regression functions comes out of the spline theory in a natural way. An appropriate value of this measure can be estimated from the data and used to constrain the estimated model to have the estimated deviation. Some convergence results and computational tricks are also discussed.