总体最小二乘准则下非线性EV模型的参数拟合方法

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英文篇名：The Method of Nonlinear EV Model Fitting Based on Total Least Squares 作者：王福昌 ; 钱小仕 ; 张艳芳 ; 任晴晴 英文作者：WANG Fu-chang;QIAN Xiao-shi;ZHANG Yan-fang;REN Qing-qing;Department of Basic Courses, Institute of Disaster Prevention; 关键词：非线性模型 ; 总体最小二乘 ; 拟合 ; 最优化方法 英文关键词：nonlinear EV model;;total least squares;;fitting;;optimization method 中文刊名：数学的实践与认识 英文刊名：Mathematics in Practice and Theory 机构：防灾科技学院基础部; 出版日期：2019-03-23 出版单位：数学的实践与认识 年：2019 期：06 基金：防灾科技学院教学团队建设(JT201707);防灾科技学院研究生课程建设与改革项目(YJG2015001);; 中央高校基本科研业务专项(ZY20140203,ZY20110101) 语种：中文; 页：145-149 页数：5 CN：11-2018/O1 ISSN：1000-0984 分类号：O212.1

摘要

在非线性回归模型参数拟合问题中,当数据中的每个变量都存在不可忽略的误差时,在普通的最小二乘准则下拟合出的参数不是最优的.按照总体最小二乘准则,以观测点到拟合曲线或拟合曲面垂直距离平方和为目标函数,然后用最优化方法搜索出使目标函数值取最小值的参数和数据点估计,从而给出求最优模型参数的算法,最后,通过计算机仿真和与文献比较,验证了提出方法的正确性.
        In nonlinear regression model parameter fitting problem, when each variable of data has negligible error, the fitting parameters by ordinary least squares criterion are not optimal. According to the total least squares criterion, the optimal objective function is sum of vertical distance squares between observation points to the fitting curve or surface fitting,and we use optimization method to find the optimal parameters and concomitant variable estimation values of minimizing objective function. The algorithm is proposed to calculate optimal parameters and concomitant variable estimation. Finally, the correctness of our new method is verified by simulations.

引文

[1]官云兰,刘绍棠,周世建等.基于整体最小二乘的稳健点云数据平面拟合[J].大地测量与地球动力学,2011, 31(5):80-83.
    [2]曹慧荣,王福昌.全最小二乘和全加权最小一乘准则下的空间直线拟合[J].计算机应用与软件,2010,27(9):111-112,127.
    [3] Boggs P T, Byrd R H, Schnabel R B. A Stable and Efficient Algorithm for Nonlinear Orthogonal Distance Regression[J]. SIAM Journal on Scientific and Statistical Computing, 1987, 8(6):1052-1078.
    [4]Li Y, Liu X F,Zhang S M. The Large Sample Theory of a Kind of nonlinear errors-in-variable regression models[J]. Progress in Natural Science, 1996, 6(6):660-666.
    [5] Li T. Estimation of nonlinear errors-in-variables models:a simulated minimum distance estimator[J]. Statistics&Probability Letters, 2000(47):243-248.
    [6] Han H, Elie T. A simple estimator for nonlinear error in variable models[J]. Journal of Econometrics,2003(117):1-19.
    [7] Wu J, Song W. On Hong-Tamer's estimator in nonlinear errors-in-variable regression models[J].Statistics and Probability Letters, 2015(97):165-175.
    [8] Li T. Robust and Consistent Estimation of Nonlinear Errors-in-Variables Models[J]. Journal of Econometrics, 2002, 110(1):1-26.
    [9]冯三营,薛留根,李高荣.非线性EV回归模型中参数的经验似然置信域[J].应用数学,2007, 20(2):400-407.