The Signal Extraction Approach to Nonlinear Regression and Spline Smoothing
本文提出一种基于信号噪声模型和卡尔曼滤波的方法，用于拟合数据点的平滑曲线（多项式样条），无需预设参数形式，可进行点预测和区间预测，计算量小且适用于大样本。
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.