线性不等式约束下一类线性模型参数估计的渐近解及其收敛性

利用交替迭代算法, 研究在线性不等式约束下具有相同参数的两个线性模型在误差方差未知条件下的参数估计问题, 得到了其参数的最小二乘估计序列及其渐近解, 并利用多元多项式方程组解的个数定理和不动点定理, 证明了此估计序列是依概率1收敛的.

Approximate Solution and Convergence of Parameter Estimation of a Linear Model with Linear Inequality Constraints

With the alternating iterative algorithm,solved parameters estimation question of mathmatic model in the case of unknown error variances,which contains two linear models with the same parameters under linear inequality constraints,was investigated and two least square estimation sequences and the approximate solutions that refer to the parameters in the model were obtained,on the basis of which via fixed-point theorem and numbers theorem of solutions of multivariate polynomial equation group it was proved that the estimation sequences are convergent in probability 1.