Best linear unbiased prediction for linear combinations in general mixed linear models

Xu-Qing Liu, Jian-Ying Rong and Xiu-Ying Liu

Journal of Multivariate Analysis, 2008, vol. 99, issue 8, 1503-1517

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.

Keywords: 62J05; 62F10; 15A04; 62B05; Mixed; linear; model; Transformed; model; Linear; combination; Best; linear; unbiased; predictor; (BLUP); Linear; sufficiency; Linear; minimal; sufficiency; Linear; completeness (search for similar items in EconPapers)
Date: 2008
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

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