约束条件下误差协方差阵的二次型估计的可容许性  

Admissibility of Quadratic Estimator for Error Covariance Matrix with Respect to Restricted Parameter Space

作　　者：龚艳红[1] 刘万荣[2] 

机构地区：[1]华南农业大学理学院,广州510640 [2]湖南师范大学数学与计算机学院,长沙410081

出　　处：《重庆师范大学学报（自然科学版）》2008年第1期47-49,63,共4页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金资助项目(No.30230210)

摘　　要：估计的可容许性一直是模型估计理论的重要部分,其主要包括系数估计的可容许性与误差估计的可容许性。随着统计模型的不断扩展与完善,各种有关的容许性理论也在不断的更新和完善之中。作为椭圆约束下一元模型中误差估计的可容许性向高维的一种推广,本文主要讨论在不等式约束条件下多元线性模型中误差协方差阵V的二次型估计的可容许性,得到了在二次型估计可容许的必要条件以及rk(x)=1与x=(1,1,…,1)T情形下可容许估计的充要条件等结果。Among the theory of estimation,admissibility of estimator is a very important part.It includes the estimator for parameter of coefficient and error.Developing with statistic model,the theory of admissibility is updated.In this paper we consider the admissibility of quadratic estimator for error covariance matrix in multivariate linear model under some inequality.We derived the necessary condition for the admissibility of a nonnegative,quadratic form estimator for error covariance matrix in the case where the error covariance V and regression parameter vector satisfy H ={（ ,V）： ^TX^TX ≤V}.Moreover, sufficient and necessary conditions are given when the design matrix X satisfy rk（X） = l and X = （ l, l ,……, l ）T. Those results are extension from unvariate linear model to multivariate linear model with respect to restricted ellipsoidal parameter space.

关 键 词：协差阵 非负二次估计 可容许性 损失函数 

分 类 号：O212.1[理学—概率论与数理统计]