不同混合线性模型下线性函数的最佳线性无偏预测相等的条件(英文)

Conditions on equalities of BLUPs for linear functions under mixed linear models

考虑一个不仅对协方差矩阵没有任何秩假设,而且对随机效应向量和随机误差向量之间的关系没有任何限制的混合线性模型.给出了线性统计量Ay是线性函数f(L,N)的最佳线性无偏预测的充要条件;同时也给出了在混合线性模型M_1下BLUP(f(L,N))仍是在混合线性模型M_2下BLUP(f(L,N))的充要条件;最后给出在两混合线性模型下BLUP(f(L,N))相等的条件.

In this paper,we consider a general mixed linear model without any rank assumptions to the covariance matrix and without any restrictions on the correlation between the random effects vector and the random errors vector.We show a new necessary and sufficient condition for linear statistic Ay to be the best linear unbiased predictor（BLUP） for the linear function of fixed effects and realized values of random effects f（L,N）.Moreover,we derive some necessary and sufficient conditions for the BLUP（f（L,N）） under M1 continue to be the BLUP（f（L,N））under M2,as well as some necessary and sufficient conditions for the equivalence of BLUP（f（L,AT）） under the two linear mixed models M1 and M2.