论文标题
非均匀B型序列的一般p频道
General P-Splines for Non-Uniform B-Splines
论文作者
论文摘要
我们提出了一个新的受惩罚的B型估计量，即通用P型，以适应不均匀间隔的打结上的不均匀B型。这是对Eilers和Marx的标准P-Spline的补充，该标准P-Sphine针对等距结上的均匀B型量度量身定制。从本质上讲，我们获得了一种新颖的一般差异惩罚，该罚款是不规则的结间隔，同时仍然易于计算和解释。这两个P型变体都可用于实践平滑，因为任何一种都可以产生比另一个更令人满意的拟合度，具体取决于所使用的结序序和数据进行分析。因此，从业人员应该在下注两者之前尝试两者，为此，我们在R Packages GPS和GPS.MGCV中实施了一般的P-Sphine。新的一般P型载序与O'Sullivan样条（或O-Spline）密切相关，该三明治公式将一般差异与衍生性惩罚联系起来。尽管两种惩罚在Wiggliness控制的数学关联和统计相似性方面似乎同样强大，但模拟研究表明，一般的P-Spline在平均平方误差方面优于O-Spline的表现，或者表现得同样好，使其成为O-Spline的优越替代。
We proposed a new penalized B-splines estimator, the general P-spline, to accommodate non-uniform B-splines on unevenly spaced knots. It is a complement to Eilers and Marx's standard P-spline tailored for uniform B-splines on equidistant knots. At its core, we derived a novel general difference penalty that accounts for irregular knot spacing, while still being easy to compute and interpret. Both P-spline variants are useful for practical smoothing, because either one can produce a more satisfactory fit than the other, depending on the knot sequence being used and the data being analyzed. Therefore, practitioners should try out both before betting on either one, for which we have implemented general P-spline in R packages gps and gps.mgcv. The new general P-spline is closely related to O'Sullivan spline (or O-spline) through a sandwich formula that links general difference penalty to derivative penalty. Though both penalties seem equally powerful in wiggliness control for their mathematical association and statistical similarity, simulation studies show that general P-spline either outperforms O-spline in terms of mean squared error, or performs equally well, making it a superior replacement of O-spline.
