| 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 |
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| 引用本文： | 丁秀芳,;宋广景.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[J].应用数学与计算数学学报,2014(4):510-517. |
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| 作者姓名： | 丁秀芳 ;宋广景 |
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| 作者单位： | [1]上海大学理学院,上海200444; [2]潍坊学院数学与信息科学学院,山东潍坊261061 |
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| 基金项目： | supported by the National Natural Science Foundation of China（11326066）;the Doctoral Program of Shandong Province（BS2013SF011）;the Shandong Province Higher Education Science and Technology Program（J14LI01）;the Key Project of Scientific Research Innovation Foundation of Shanghai Municipal Education Commission（13ZZ080） |
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| 摘 要： | 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M1下BLUP（f（L,N））仍是在混合线性模型M2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.
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| 关 键 词： | 一般混合线性模型 最佳线性无偏估计 最佳线性无偏预测 |
Conditions on equalities of BLUPs for linear functions under mixed linear models |
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| Institution: | DING Xiu-fang,SONG Guang-jing(1. College of Sciences, Shanghai University, Shanghai 200444, China; 2. School of Mathematics and Information Sciences, Weifang University Weifang 261061, Shandong Province, China) |
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| Abstract: | 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. |
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| Keywords: | general mixed linear model best linear unbiased estimator（BLUE） best linear unbiased predictor（BLUP） |
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