On relations between BLUPs under two transformed linear random-effects models

Some Remarks on the Equalities of Predictors in Linear Mixed Models

“…If G = 0 and H = 0, Fy corresponds the best linear unbiased estimator (BLUE) of Jα, denoted by BLUE M (Jα), under M. Although predictors under LMMs and their TLMMs have different properties, observable random vectors in TLMMs may contain enough information to predict unknown vectors under LMMs. Within this context, establishing the results on the relations between these models can be considered as one of the important issues among others in linear regression analysis; see, e.g., [4,7,22,24]. We may also refer to the following works on relations between predictors under different LMMs; [2, 8-10, 12, 25].…”

“…Various rank formulas for partitioned matrices provide us effective tools for simplifying complicated matrix expressions composed by matrices and their Moore-Penrose generalized inverses. The rank of matrices are one of the basic concepts in linear algebra and matrix theory, and also plays an essential role in problems on establishing equalities and inequalities occurred in statistical analysis; see, e.g., [4,7,17,26].…”