非线性约束条件的平稳自回归模型的L_1-估计

L_1-Estimators of Stationary Autoregressive Model with Nonlinear Constraints

L1估计是统计问题中一个重要估计 .时间序列模型的L1估计问题是非常重要的 ,这些估计量的多种性质都被研究过 .许多统计学者讨论了它在无约束条件情况下的估计问题及其有关性质 ,且得到了很好的结果 ,然而 ,仍有一些基本问题有待解决 .本文讨论了平稳自回归模型的L1估计在非线性约束条件下的渐近性质 .该约束条件是由非线性等式和不等式给出 .这种估计问题属于随机优化问题 .用最优化的方法克服非线性约束问题在估计研究上的困难 ,为估计提供一个新的途径 ,并得到了L1估计问题的相关结果 .

L 1-estimator is an important estimator in statistic problems. L 1-estimation for time series is very important. Some properties of these estimators have been studied. Many statistics scholars have studied estimator problems and their properties with absence of restriction and reached good conclusions. However, some basic problems on this subject are left open. This paper studies the asymptotic behavior of L 1-estimator of stationary autoregressive models with nonlinear constraint. Here the constraint is given by nonlinear equalities and inequalities. This kind of estimation problem is a stochastic optimization problem. Optimization methods are used to overcome the difficulty caused by nonlinear constraint and this paper also provides relevant conclusions of this problem.