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- Title
Two competing linear random-effects models and their connections.
- Authors
Lu, Changli; Sun, Yuqin; Tian, Yongge
- Abstract
Assume that an observed random vector is represented in two alternative linear random-effects models (LRMs). In this case, the results of statistical inference under the two LRMs are not necessarily the same. The objective of this paper is to study the performance of the best linear unbiased predictors/best linear unbiased estimators (BLUPs/BLUEs) of all unknown parameters in two LRMs under most general assumptions on the covariance matrices of the random-effects terms and error terms. We establish necessary and sufficient conditions for the BLUPs/BLUEs to be equivalent under the two LRMs using some well-known formulas for calculating ranks of matrices and their generalized inverses, and also present various consequences and conclusions on some special special cases of LRMs.
- Subjects
RANDOM variables; VECTORS (Calculus); COVARIANCE matrices; MATRICES (Mathematics); MATHEMATICAL equivalence
- Publication
Statistical Papers, 2018, Vol 59, Issue 3, p1101
- ISSN
0932-5026
- Publication type
Article
- DOI
10.1007/s00362-016-0806-3