【摘要】 本文考虑了如下的一般多元线性模型■中未知参数阵B与∑的线性函数tr(D＇B)+tr(C∑)的联立估计问题,给出了tr(D＇B~*)+tr(C∑~*)是其期望值的一致最小方差不变二次加线性无偏估计(UM-VIQLUE)的充要条件,这是一个类似于多元许定理的结果,其中B~*与∑~*分别是B与∑的在一定意义下的最小二乘估计.更多还原

【Abstract】 The simultaneous estimation of linear function of regression coefficient matrix B and covariance matrix ∑ is investigated in the following general multivariate linear model Some necessary and sufficient conditions are derived for tr (D’B~*)+ tr (C∑~*) to be UMVIQLUE (uniformly minimum variance invariant quadratic plus linear unbiased estimate) of its expectation, where B~* and ∑~* are LSE (least squares estimate) of B and ∑ in a sense respectively. This result is similar to Mu- ltivariate Hsu’s Theorem.更多还原