Best linear unbiased prediction for linear combinations in general mixed linear models |
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Authors: | Xu-Qing Liu Jian-Ying Rong |
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Affiliation: | a Department of Computing Science, Huaiyin Institute of Technology, Huai’an 223001, PR China b Department of Foundation Courses, Huai’an College of Information Technology, Huai’an 223003, PR China c Department of Mathematics, Heze University, Heze 274015, PR China |
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Abstract: | The general mixed linear model can be written as . In this paper, we mainly deal with two problems. Firstly, the problem of predicting a general linear combination of fixed effects and realized values of random effects in a general mixed linear model is considered and an explicit representation of the best linear unbiased predictor (BLUP) is derived. In addition, we apply the resulting conclusion to several special models and offer an alternative to characterization of BLUP. Secondly, we recall the notion of linear sufficiency and consider it as regards the BLUP problem and characterize it in several different ways. Further, we study the concepts of linear sufficiency, linear minimal sufficiency and linear completeness, and give relations among them. Finally, four concluding remarks are given. |
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Keywords: | 62J05 62F10 15A04 62B05 |
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