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自动选取多非线性参数初始值的循环搜索法
引用本文:朱珉仁,李勇.自动选取多非线性参数初始值的循环搜索法[J].高等学校计算数学学报,2006,28(3):252-261.
作者姓名:朱珉仁  李勇
作者单位:1. 东南大学数学系,南京,210096
2. 香港中文大学统计系,香港
基金项目:东南大学数学系韦博成教授的热心指导和鼓励,以及审稿人的修改建议,大大帮助提高了本文.在此表示衷心的感谢.
摘    要:1几何中心化加权最小二乘法给定观测数据集(x_i,y_i),i=1,2,…,n.(1.1)欲拟合加权非线性模型y_i=f(x_i,θ) ε_i,(1.2)其中模型函数f的参数为θ=(θ_1,…,θ_p)~T,随机观测误差项满足ε_i~N0,(?)~2m(z_i,λ)],(1.3) m(z_i,λ)为已知正值函数,z_i可以是x_i,也可以是μ_i=f(x_i,θ)或二者的组合,λ为权参数,而(?)~2为未知的方差参数,λ和θ可统称为模型参数.模型的似然函数为

关 键 词:循环搜索法  非线性参数  自动选取  初始值  加权最小二乘法  中心化  数据集
收稿时间:10 8 2004 12:00AM
修稿时间:2004-10-08

A CYCLIC SEARCH METHOD CHOOSING THE INITIAL VALUE OF SEVERAL NONLINEAR PARAMETERS AUTOMATICALLY
Zhu Minren,Li Yong.A CYCLIC SEARCH METHOD CHOOSING THE INITIAL VALUE OF SEVERAL NONLINEAR PARAMETERS AUTOMATICALLY[J].Numerical Mathematics A Journal of Chinese Universities,2006,28(3):252-261.
Authors:Zhu Minren  Li Yong
Institution:1.Department of Mathematics, Southeast University, Nanjing 210096 2.Department of Statistics, HongKong Chinese University, HongKong
Abstract:In nonlinear regression analysis,one of the most important problems that the iterative algorithms for computing the MLE often meet is to choose the initial value.A bad initial value can often make the algorithm lose effect.However, until now there are still no good methods to solve the problem.In this paper,as to the MLE problem of the weighted nonlinear regression model,we propose geometric centralized weighted least square method and use the cyclic search method to automatically choose the initial value of several nonlinear parameters through the observed data.We make the algorithm less dependent on the initial value and figure out how to find the initial value concretely.At the end,several numerical examples are given in order to explain the application of this algorithm.
Keywords:weighted nonlinear regression model  MLE  geometric centralized weighted least square method  a cyclic search method
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