非线性回归模型M估计的迭代公式及其收敛性

THE ISERATION PROCEDURE AND ITS CONVERGENCE OF M ESTIMATOR IN NONLINEAR REGRESSION

本文研究了非线性回归模型M估计的Gauss-Newton迭代公式及其改进形式的收敛性问题。把Jeunrich和Gallant等人关于最小二乘估计的结果推广到M估计的情形。本文的证明显示,这些结果还可以推广到更广泛的模型和更一般的估计。本文的实例说明,改进的Gauss-Newton迭代法对于求解非线性回归的M估计是比较有效的,M估计对于消除异常点的影响育显著的作用。

Gauss-Newton iteration method and modified G-N method and their conyergence of M estimator in nonlinear regression are discussed in this paper. We generalized the resalts of Jennrich([6])and Gallant et. ale ([4])from least squares estimator to M estimator. The numerical example shows that the modified G-N method is more preferable and the M estimator is very helpful to reduce the effects of outliers.