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中文摘要：
考虑方差分量（混合线性）模型y=Xβ＋U1ξ1＋U2ξ2＋…＋Ukξk，这里Xn×p，Ui，n×ti为已知设计矩阵，βp×1是固定效应，ξi是ti×1随机效应向量，满足E（ξi）=0，cov（ξi）=σi^2Ⅰti，ξi都不相关．往往Uk=Ⅰn，ξk=ek，即最后一项为随机误差，β∈R^p和σi^2〉0（i=1，2，…，k）为未知参数．我们考虑β的可估函数Sβ，选取二次损失函数L（d，Sβ）=（d-Sβ）＇（d-Sβ）/∑i=1^k ciσi^2＋β＇X＇Vk^-1Xβ，然后在线性估计类中给出Sβ的惟一的minimax估计．
英文摘要：
Consider the mixed linear model y=Xβ＋U1ξ1＋U2ξ3＋…＋Ukξk,E（ξi）=0,cov（ξi,ξj）=0,i≠j,cov（ξi,ξj）=σi^2Vi,i,j=1,2,…,k, vector, where y is a random n ×1 column n×1 column vector,Xn×p,Ui,n×ti,and Vi≥0 are known.β∈R^p,σi^2〉0 are parmeters ,i=1,2,…,k.Choose a loss function L（d,Sβ）=（d-Sβ）＇（d-Sβ）/∑i=1^k ciσi^2＋β＇X＇Vk^-1XB We obtain the unipue minimax estimator of linear estimable functions Sβin the class of linear estimatiors.
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