Flexible smoothing with B-splines and penalties
Flexible smoothing with B-splines and penalties
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DOI：
10.1214/ss/1038425655
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发表时间：
1996-05-01
影响因子：
5.7
通讯作者：
Marx, BD
中科院分区：
文献类型：
--
作者：
Eilers, PHC;Marx, BD
B样条对于非参数建模是有吸引力的，但是选择最佳的节点数量和位置是一项复杂的任务。可以使用等距结，但它们的小且离散的数量仅允许对平滑度和拟合的有限控制。我们建议使用一个相对较大数量的节点和相邻的B-样条的系数差罚。我们显示连接到熟悉的样条惩罚的平方二阶导数的积分。一个简短的概述B-样条，其建设和惩罚的可能性。我们讨论了惩罚B样条的性质，并提出了各种标准的最佳惩罚参数的选择。非参数逻辑回归，密度估计和散点图平滑作为例子。计算的一些细节。
B-splines are attractive for nonparametric modelling, but choosing the optimal number and positions of knots is a complex task. Equidistant knots can be used, but their small and discrete number allows only limited control over smoothness and fit. We propose to use a relatively large number of knots and a difference penalty on coefficients of adjacent B-splines. We show connections to the familiar spline penalty on the integral of the squared second derivative. A short overview of B-splines, of their construction and of penalized likelihood is presented. We discuss properties of penalized B-splines and propose various criteria for the choice of an optimal penalty parameter. Nonparametric logistic regression, density estimation and scatterplot smoothing are used as examples. Some details of the computations are presented.