任意秩有限总体中无偏预测和估计的构造关系

Unbiased prediction and its construction relationship to unbiased estimation in finite populations with arbitrary rank

研究了有限总体均值向量的无偏估计和线性可预测变量的无偏预测之间的关系,利用分块矩阵广义逆直接对加权风险函数进行分解,提出了一种由均值向量的无偏估计来构造无偏预测的新方法,并找到了它们之间的构造关系.特别地,线性可预测变量的最优线性无偏预测(BLUP)可由均值向量的最佳线性无偏估计(BLUE)惟一地表示(有关惟一性在几乎处处意义下理解).

The unbiased predictor of linear predictable variable and its relationship to unbiased estimator of mean vector in finite populations are investigated. Based on generalized inverse of partitioned matrix in weighted loss function, unbiased predictors can be constructed by unbiased estimators of mean vector. Furthermore, this paper derives the construction relations between unbiased prediction and unbiased estimation. Especially, the BLUP of linear predictable variable can be formulated by BLUE of mean vector,which is unique in the sense ＂almost everywhere＂