Linear Estimation with an Incorrect Dispersion Matrix in Linear Models with a Common Linear Part
研究了在具有公共线性部分的线性模型中，当散布矩阵设定错误时，哪些非负定矩阵能使BLUE保持不变，并给出了方差分量模型中可估函数存在BLUE的条件。
Abstract The linear model (Y, Xβ, V), where X is any matrix satisfying the conditions ℛ (U) ⊂ ℛ (X) and ℛ (A′) ⊂ ℛ (X′), is considered, U and A being known matrices and ℛ (·) denoting range space. Nonnegative definite matrices V, for which every linear representation or some linear representation of the BLUE of Aβ under (Y, Xβ, V 1) continues to be its BLUE under (Y, Xβ, V) for every such matrix X, are characterized. Conditions under which estimable linear parametric functions admit a BLUE for the variance components model are also given.