带约束非线性回归的最小二乘估计的极限分布

非线性回归的ＬＳ 估计问题是一类重要的统计问题。关于带约束条件的非线性回归问题也有不少人进行了研究， 但大部分文章局限于线性约束。最近运用随机最优化的工具对非线性约束进行了探讨。并在线性独立条件下得到ＬＳ 估计的极限分布。本文将条件放宽到Ｍ－ Ｆ 条件， 得到同样的结论。

Asympotoics of Least-squares Estimators for Constrained Nonlinear Regression

The LS-estimator in nonlinear regression problems is an important statistical estimator problem.Many authors have studied the constrainded regression problems, but most of them are restricted to linear constraints.Recently some people made use of methods in stochastic optimization to study nonlinear regression problems with nonlinear constraints, and derived the asymptotic distribution of LS-estimators under linear independence condition.In this paper we use M-F condition instead of linear independence condition, we will derive the same results.