自适应局部惩罚样条回归模型探讨

发布时间：2018-07-12 20:03

本文选题：方差 + 局部惩罚样条　；参考：《统计与决策》2017年21期

【摘要】：在惩罚样条回归方法中,截断幂基系数的惩罚权重是相等的,这导致在数据具有局部异质性时不能很好地去拟合原函数。文章以结点两端数据点的方差构造了一种新的局部惩罚样条回归方法,能够很好地解决数据具有局部异质性的问题。该方法对数据波动较小的区域给予较大的惩罚,而对数据波动较大的区域给予较小的惩罚,从而实现惩罚的局部性。通过模拟的结果可知,当数据具有局部异质性时,构造的新的局部惩罚样条比整体惩罚样条和光滑样条具有更好的拟合效果。
[Abstract]:In the penalty spline regression method, the penalty weights of the truncated power base coefficients are equal, which leads to the failure to fit the original function well when the data has local heterogeneity. In this paper, a new local penalty spline regression method based on the variance of data points at both ends of nodes is proposed, which can solve the problem of local heterogeneity of data. In this method, the region with less data fluctuation is punished more, and the region with large data fluctuation is punished less, so that the punishment can be localized. The simulation results show that the new local penalty spline is better than the global penalty spline and the smooth spline when the data has local heterogeneity.
【作者单位】：安徽大学数学科学学院;安徽大学商学院;
【基金】：国家自然科学基金(天元基金)资助项目(11026076) 安徽大学大学生科研训练计划项目(J18520205)
【分类号】：O212.1

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