Degrees-of-freedom tests for smoothing splines
Degrees-of-freedom tests for smoothing splines
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DOI：
10.1093/biomet/89.2.251
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发表时间：
2002-06-01
期刊：
影响因子：
2.7
通讯作者：
Hastie, T
中科院分区：
文献类型：
--
作者：
Cantoni, E;Hastie, T
在用光滑样条函数估计函数时，用户面临着如何选择光滑参数的问题。有几种技术可用于根据某些最优性标准选择此参数。在这里，我们采取不同的观点，我们提出了一种在两种选择之间进行选择的技术，例如允许两种不同程度的自由度。这个问题是在一个混合效应模型的框架，其假设确保所得到的估计是无偏的。提出了一种似然比型检验统计量，并导出了它的精确分布。线性和总体效应检验直接遵循。然后，我们将这一想法扩展到添加剂模型，它提供了一个更有吸引力的替代方案比多参数优化，并在那里它给出了精确的分布结果，可用于分析的偏差类型的方法。真实的数据和电平和功率的模拟研究的例子完成了论文。
When using smoothing splines to estimate a function, the user faces the problem of choosing the smoothing parameter. Several techniques are available for selecting this parameter according to certain optimality criteria. Here, we take a different point of view and we propose a technique for choosing between two alternatives, for example allowing for two different levels of degrees of freedom. The problem is addressed in the framework of a mixed-effects model, whose assumptions ensure that the resulting estimator is unbiased. A likelihood-ratio-type test statistic is proposed, and its exact distribution is derived. Tests of linearity and overall effect follow directly. We then extend this idea to additive models where it provides a more attractive alternative than multi-parameter optimisation, and where it gives exact distributional results that can be used in an analysis-of-deviance-type approach. Examples on real data and a simulation study of level and power complete the paper.