﻿ 基于双边核估计的保持跳跃曲线回归过程 A Jump-Preserving Curve Regression Procedure Based on Bilateral Kernel Estimation

Statistical and Application
Vol.04 No.04(2015), Article ID:16725,13 pages
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

Received: Dec. 10th, 2015; accepted: Dec. 28th, 2015; published: Dec. 31st, 2015

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

1. 引言

2. 跳跃回归模型

(1)

(2)

3. 基于双边核的保跳曲线拟合过程

(3)

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2)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

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(19)

， (20)

, (21)

(22)

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4. 数值实验

4.1. 仿真模拟

Figure 1. Original image of f1(x)

Figure 2. Comparison among different estimation methods of f1(x)

Figure 3. Confidence interval of f1(x)

Figure 4. f1(x) MSE of local piecewise linear bilateral Kernel estimation under different iteration times

Table 1. MSE value for different estimation method of f1(x)

4.2. 数值实例

Figure 5. Original image of f2(x)

Figure 6. Comparison among different estimation methods of f2(x)

Figure 7. Confidence Interval of f2(x)

Table 2. MSE value for different estimation method of f2(x)

Figure 8. f2(x) MSE of local piecewise linear bilateral Kernel estimation under different iteration times

5. 讨论

5.1. 光滑性

5.2. 带宽选择

Figure 9. Real data image and its fitting result

5.3. 迭代次数

A Jump-Preserving Curve Regression Procedure Based on Bilateral Kernel Estimation[J]. 统计学与应用, 2015, 04(04): 335-347. http://dx.doi.org/10.12677/SA.2015.44037

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19. NOTES

*通讯作者。