二次损失下可估函数的线性MINIMAX估计的性质及其应用

THE PROPERTIES OF THE LINEAR MINIMAX ESTIMATE UNDERA QUADRATIC LOSS AND ITS APPLICATION

对于线性模型Ｙ～（Ｘβ，σ２Ｖ）中的可估函数Ｓβ，本文在二次损失Ｌ（β，σ２；ｄ）＝（ｄ－Ｓβ）′ｄ－Ｓβ）／（σ２＋β′Ｘ′Ｖ－１Ｘβ）下讨论了线性估计类中的ｍｉｎｉｍａｘ估计的性质，并利用这些性质徐兴忠得到的线性ｍｉｎｉｍａｘ估计及其最大风险的表达式提供了一个相对简短的证明．

Given a linear model EY=Xβ,CovY=σ2V,the properties of the minimax estimate of the estimable function Sβ in the class of homogeneous linear estimators under a given queadtatic loss function are discussedThe properties are applied to provide a simple proof for the known expressions of the unique linear minimax estimate and its maximum risk