an:06670291
Zbl 1358.15012
Tian, Yongge; Jiang, Bo
An algebraic study of BLUPs under two linear random-effects models with correlated covariance matrices
EN
Linear Multilinear Algebra 64, No. 12, 2351-2367 (2016).
00360540
2016
j
15A24 15A09 62H12 62J05 62J10
linear random-effects model; sub-sample model; covariance matrix; rank formula; linear unbiased predictors; linear matrix equations
Authors' abstract: Assume that a pair of general linear random-effects models (LRMs) is given with a correlated covariance matrix for their error terms. This paper presents an algebraic approach to the statistical analysis and inference of the two correlated LRMs using some state-of-the-art formulas in linear algebra and matrix theory. It is first shown that the best linear unbiased predictors (BLUPs) of all unknown parameters under LRMs can be determined by certain linear matrix equations, and thus the BLUPs under the two LRMs can be obtained in exact algebraic expressions. We also discuss algebraical and statistical properties of the BLUPs, as well as some additive decompositions of the BLUPs. In particular, we present necessary and sufficient conditions for the separated and simultaneous BLUPs to be equivalent. The whole work provides direct access to a very simple algebraic treatment of predictors/estimators under two LRMs with correlated covariance matrices.
Chen Sheng (Harbin)