基于双边核估计的保持跳跃曲线回归过程基于双边核估计的保持跳跃曲线回归过程.pdf

Statistical and Application 统计学与应用, 2015, 4(4), 335-347 Published Online December 2015 in Hans. /journal/sa /10.12677/sa.2015.44037 A Jump-Preserving Curve Regression Procedure Based on Bilateral Kernel Estimation * Yiran Li, Xingfang Huang , Jiazhao Ding, Xuan Chen Department of Mathematics, Southeast University, Nanjing Jiangsu th th st Received: Dec. 10 , 2015; accepted: Dec. 28 , 2015; published: Dec. 31 , 2015 Copyright © 2015 by authors and Hans Publishers Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). /licenses/by/4.0/ Abstract 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. Keywords Curve Fitting Procedure, Jump-Preserving, Bilateral Kernel Estimation, Weighted Residual Sums of Squares, Discontinuous Curve 基于双边核估计的保持跳跃曲线回归过程 * 李怡然，黄性芳 ，丁嘉沼，陈 旋