论文标题
通过自适应样条拟合的变化系数模型
Varying Coefficient Model via Adaptive Spline Fitting
论文作者
论文摘要
不同的系数模型已受到研究人员的广泛关注，因为它是用于非参数建模的强大降低工具。装有多项式样条的大多数现有变化的系数模型假定等距结，并将结数作为超参数。但是，施加等距的结似乎太僵硬了，并且系统地确定最佳结数也是一个挑战。在本文中，我们通过使用自适应选择和预测特异性结的多项式花键来应对这一挑战，以适合不同系数模型中的系数。提出了有效的动态编程算法来找到最佳解决方案。数值结果表明，与等距样条拟合方法相比，新方法可以实现系数的平均平方误差明显较小。
The varying coefficient model has received broad attention from researchers as it is a powerful dimension reduction tool for non-parametric modeling. Most existing varying coefficient models fitted with polynomial spline assume equidistant knots and take the number of knots as the hyperparameter. However, imposing equidistant knots appears to be too rigid, and determining the optimal number of knots systematically is also a challenge. In this article, we deal with this challenge by utilizing polynomial splines with adaptively selected and predictor-specific knots to fit the coefficients in varying coefficient models. An efficient dynamic programming algorithm is proposed to find the optimal solution. Numerical results show that the new method can achieve significantly smaller mean squared errors for coefficients compared with the equidistant spline fitting method.
