基于径向基的自适应惩罚样条回归模型

发布时间：2018-03-29 01:11

本文选题：非参回归　切入点：惩罚样条　出处：《高校应用数学学报A辑》2017年03期

【摘要】：传统惩罚样条回归模型中惩罚项的设置未考虑数据的空间异质性,因而对复杂数据的拟合缺乏自适应性.文章通过对径向基函数的几何意义分析,以节点两侧相邻区域内数据点的纵向极差为基础,构造局部惩罚权重向量并加入到约束回归模型的惩罚项中,构造了基于径向基的自适应惩罚样条回归模型.新模型在观测数据波动较大的区域,给予拟合曲线较小的惩罚,而在观测数据波动较小的区域,给予拟合曲线较大的惩罚,从而使拟合曲线能自适应地反映观测数据的局部变化特征.模拟和应用结果显示新模型的拟合效果显著优于传统的惩罚样条回归模型.
[Abstract]:In the traditional penalty spline regression model, the penalty term is set without considering the spatial heterogeneity of the data, so the fitting of the complex data is not adaptive. The geometric meaning of the radial basis function is analyzed in this paper. Based on the longitudinal range of the data points in the adjacent region on both sides of the node, the local penalty weight vector is constructed and added to the penalty term of the constrained regression model. An adaptive penalty spline regression model based on radial basis is constructed. The new model punishes small fitting curve in the region with large fluctuation of observed data, while in the region with less fluctuation of observed data, the new model is penalized by larger fitting curve. The simulation and application results show that the fitting effect of the new model is better than that of the traditional penalty spline regression model.
【作者单位】：安徽大学数学科学学院;
【基金】：国家自然科学基金(11671012) 安徽省自然科学基金(1708085MF163) 安徽省高校自然科学基金(KJ2017A028;KJ2017A024) 安徽大学数学科学学院开放课题(Y01002431)
【分类号】：O212.1

【相似文献】