基于双边核估计的保持跳跃曲线回归过程

It is well known that curve regression is very important in many applications. However, since data collection procedures are disturbed by errors, traditional curve regression methods cannot play well in jump points. This paper proposes a jump-preserving curve fitting procedure, which is based on bilateral kernel estimation. Kernel functions are not only added to x-axis, but also added to y-axis. Then, we estimate given points from left side, right side and whole neighborhood. Weighted residual sums of squares are calculated to compare. The estimate with smaller weighted residual sums of squares is selected as the final estimate of the given point, so that we can achieve jump- preserving while not to detect jump points at first. Numerical simulation and real data analysis demonstrate the feasibility and efficiency of this method.

众所周知，曲线回归在许多应用中非常重要。然而，由于数据采集过程受到误差干扰，传统的曲线回归方法在跳跃点处效果不佳。本文提出了一种基于双边核估计的保跳跃曲线拟合方法。不仅在x轴上添加核函数，在y轴上也添加核函数。然后，我们从左侧、右侧和整个邻域对给定的点进行估计。计算加权残差平方和进行比较，选择加权残差平方和较小的估计值作为给定点的最终估计值，这样我们可以在一开始不检测跳跃点的情况下实现保跳跃。数值模拟和实际数据分析证明了该方法的可行性和有效性。