多元回归系数的所有k-容许估计

ALL k-ADMISSIBLE ESTIMATORS OF MULTIVARIATE REGRESSION COEFFICIENTS

对于多元线性模型Y～N（XΘ，）（已知）中的可估函数SXΘ的估计问题，取损失函数为（δ－SXΘ）'（δ－SXΘ）．用风险函数矩阵的前k个顺序特征值之和作为比较不同估计的风险函数大小的标准，我们可定义所谓的"k－容许估计"．本文得到了SXΘ的线性估计AY＋D在一切估计类中k－容许的充要条件．

For the estimation problem of estimable function SXΘ in the multivariate linear model Y ~ N (XΘ,Im ), is known, the loss function is selected as (δ- SXΘ)'(δ- SXΘ). Using the sum of the first k eigenvalues of the risk function as the standard for comparison of the size of risk function R(δ, SXΘ). Then we can define the so-called k-admissibility. This paper has obtained the necessary and sufficient conditions for the estimator LY + D of SXΘ to be k-admissible in the class of all estimators.