论文标题
多项式样条回归：理论和应用
Polynomial spline regression: Theory and Application
论文作者
论文摘要
为了处理预测因子和响应之间的非线性关系，我们可以使用转换使数据看起来是线性或近似线性的。但是，在实践中，转换方法可能是无效的，并且使用可以自动处理非线性行为的灵活回归技术可能更有效。一种方法是多项式样条（PS）回归。因为可能需要的样条回归模型的数量是许多选择最佳选择的有效策略。这项研究以理论和实用的方式研究了不同的样条回归模型（基于截短的功率，b-Spline和p-spline）的不同样条回归模型。我们专注于基本概念，因为在理论上，样条回归在理论上是丰富的。特别是，我们专注于使用交叉验证（CV）而不是解释的预测，因为多项式花键在解释方面具有挑战性。我们根据真实数据集比较不同的PS模型，并得出结论，P-Spline模型是最好的。
To deal with non-linear relations between the predictors and the response, we can use transformations to make the data look linear or approximately linear. In practice, however, transformation methods may be ineffective, and it may be more efficient to use flexible regression techniques that can automatically handle nonlinear behavior. One such method is the Polynomial Spline (PS) regression. Because the number of possible spline regression models is many, efficient strategies for choosing the best one are required. This study investigates the different spline regression models (Polynomial Spline based on Truncated Power, B-spline, and P-Spline) in theoretical and practical ways. We focus on the fundamental concepts as the spline regression is theoretically rich. In particular, we focus on the prediction using cross-validation (CV) rather than interpretation, as polynomial splines are challenging to interpret. We compare different PS models based on a real data set and conclude that the P-spline model is the best.
