中文摘要：

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．

英文摘要：

Classical penalized regression model is inadequate of adaptivity for fitting complex data because that the spatial heterogeneity of observation data is not considered by the penalized term. According to the geometric meaning of radial basis, the local penalization vector based on the ranges of the data around each knot is constructed and added into the penalized term of the model. This new adaptive penalized spline regression model via radial basis gives less penalization to fitted curve where the observation data is volatile and more penalization to fitted curve where the observation data is flat, which makes the model adaptive to the local characterization of the sample points. Simulations and application show the fitting effect based on new model outperforms classical penalized spline regression model.