矩阵损失下有限总体中的局部条件线性Minimax预测及唯一性

The Partial Condictional Linear Minimax Prediction in Finite Populations under Matrix Loss Function

对于任意秩有限总体,在矩阵损失下,有关文献给出了线性预测函数的局部极大极小性。考虑带线性等式约束的线性模型y=Xβ+eHβ=0E(e)=0Cov(e)=σ2V。本文将在适当的假设下,得到线性可预测函数在一切预测类中任意秩有限总体的条件可预测变量的唯一局部条件线性Minimax预测(唯一性在几乎处处意义下理解)。

Under the matrix loss function, the partial Minimax property of linear predictable variable in finite populations with arbitrary Rank was obtained in the literature. Consider linear model with linear equality constraints {Cov（e）=σ^2V^E（e）=0^Hβ=0^y=Xβ＋e In this paper, the unique partial conditional linear Minimax predictor in the class of all predictors is obtained under suitable hypotheses in the finite population with arbitrary rank. （the uniqueness is comprehended in the sense＂ almost everywhere＂）.