The Signal Extraction Approach to Nonlinear Regression and Spline Smoothing
The Signal Extraction Approach to Nonlinear Regression and Spline Smoothing
复制标题
非线性回归和样条平滑的信号提取方法
DOI：
--
复制
发表时间：
1983
期刊：
影响因子：
--
通讯作者：
C. Ansley
中科院分区：
文献类型：
--
作者：
W. E. Wecker;C. Ansley
本文展示了如何将一条光滑的曲线(多项式样条)拟合到数据值对(yi，xi)。不需要事先指定曲线的参数函数形式。得到的曲线可以用来描述数据的模式，并预测给定x的未知值y。可以产生点估计和区间估计。该方法简单易用，计算要求适中，即使在大样本情况下也是如此。我们的方法是基于数据的信噪比模型的最大似然估计。我们使用卡尔曼滤波来评估似然函数，并取得了比以前解决该问题的方法显著的计算优势。
Abstract This article shows how to fit a smooth curve (polynomial spline) to pairs of data values (yi, xi ). Prior specification of a parametric functional form for the curve is not required. The resulting curve can be used to describe the pattern of the data, and to predict unknown values of y given x. Both point and interval estimates are produced. The method is easy to use, and the computational requirements are modest, even for large sample sizes. Our method is based on maximum likelihood estimation of a signal-in-noise model of the data. We use the Kalman filter to evaluate the likelihood function and achieve significant computational advantages over previous approaches to this problem.