有约束错误指定模型下的优化问题

Additional Remarks on a Superiority Problem in Misspecified Restricted Singular Linear Models

文 [1 ]利用文 [3]的结果证明了一般有约束线性模型下参数的最优估计的方差协方差阵与有约束错误指定模型下最优估计的方差协方差阵间差是非负定的充分条件 [2 ]也是必要的 .更进一步 ,文 [4]将 [1 ]中的定理 1推广到奇异线性模型上 .该文的主要目的是证明了 [2 ]的猜想在奇异线性模型中也是正确的 ,同时 ,推广了 [1 ]中的定理 2 .

When the covariance matrix of the disturbance vector in the general linear model is misspecified, Gross, Trenkler and Liski (1998) showed Razzaghi's (1987) result that sufficient condition for nonnegative definitness of the covariance matrix difference of competing estimators is also necessary by applying a result of Kabe and Gupta (1989). Further, Zhang and Liu (2000) extended the Theorem 1 of Gross, Trenkler and Liski to the singular linear model using matrix inequality and subspace relations. The aim of this paper is to prove the conjecture which Razzaghi (1987) made is true in misspecified restricted singular linear model and strengthen Theorem 2 of Gross, Trenkler and Liski by giving the necessary and sufficient conditions for nonnegative definiteness of the covariance matrix difference in the singular linear model.