TY - JOUR

T1 - Joining models with commutative orthogonal block structure

AU - Santos, Carla

AU - Nunes, Célia

AU - Dias, Cristina

AU - Mexia, João Tiago

N1 - Sem PDF.
national founds of FCT - Foundation for Science and Technology (UID/MAT/00297/2013; UID/MAT/00212/2013)

PY - 2017/3/15

Y1 - 2017/3/15

N2 - Mixed linear models are a versatile and powerful tool for analysing data collected in experiments in several areas. A mixed model is a model with orthogonal block structure, OBS, when its variance–covariance matrix is of all the positive semi-definite linear combinations of known pairwise orthogonal orthogonal projection matrices that add up to the identity matrix. Models with commutative orthogonal block structure, COBS, are a special case of OBS in which the orthogonal projection matrix on the space spanned by the mean vector commutes with the variance–covariance matrix. Using the algebraic structure of COBS, based on Commutative Jordan algebras of symmetric matrices, and the Cartesian product we build up complex models from simpler ones through joining, in order to analyse together models obtained independently. This commutativity condition of COBS is a necessary and sufficient condition for the least square estimators, LSE, to be best linear unbiased estimators, BLUE, whatever the variance components. Since joining COBS we obtain new COBS, the good properties of estimators hold for the joined models.

AB - Mixed linear models are a versatile and powerful tool for analysing data collected in experiments in several areas. A mixed model is a model with orthogonal block structure, OBS, when its variance–covariance matrix is of all the positive semi-definite linear combinations of known pairwise orthogonal orthogonal projection matrices that add up to the identity matrix. Models with commutative orthogonal block structure, COBS, are a special case of OBS in which the orthogonal projection matrix on the space spanned by the mean vector commutes with the variance–covariance matrix. Using the algebraic structure of COBS, based on Commutative Jordan algebras of symmetric matrices, and the Cartesian product we build up complex models from simpler ones through joining, in order to analyse together models obtained independently. This commutativity condition of COBS is a necessary and sufficient condition for the least square estimators, LSE, to be best linear unbiased estimators, BLUE, whatever the variance components. Since joining COBS we obtain new COBS, the good properties of estimators hold for the joined models.

KW - Jordan algebra

KW - Mixed models

KW - Models joining

KW - Models with commutative orthogonal block structure

UR - http://www.scopus.com/inward/record.url?scp=85006976517&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2016.12.019

DO - 10.1016/j.laa.2016.12.019

M3 - Article

AN - SCOPUS:85006976517

VL - 517

SP - 235

EP - 245

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -