基于先验信息的改进随机约束两参数估计

Improved Stochastic Restricted Two-Parameter Estimation Based on Prior Information

摘要: 本文主要针对一般线性模型中存在复共线性的情况，结合随机约束条件下的混合估计和基于先验信息的两参数估计提出了一种新的有偏估计，即随机约束改进两参数估计。并在均方误差矩阵准则的意义下研究了随机约束改进两参数估计相对于两参数估计、改进两参数估计混合估计、随机约束岭估计和随机约束两参数估计的优良性。进一步，讨论了偏置参数的选择。同时，通过一个数值算例对所提出的估计的性能进行了说明。

Abstract: This paper mainly aims at the situation where there is complex collinearity in the general linear model. Combining the mixed estimator under the condition of stochastic restricted and the two-parameter estimator of parameter vectors based on prior information, a new biased estimator is proposed, that is, the stochastic constrained modified two-parameter estimator. In the sense of mean square error matrix criterion, the superiority of stochastic constrained modified two-parameter estimator relative to two-parameter estimator, modified two-parameter estimator, mixed estimator, stochastic restricted ridge estimator and stochastic restricted two-parameter estimator are studied. Further, the selection of bias parameters is discussed. At the same time, the performance of the proposed estimator is explained through a numerical example.