TY - JOUR

T1 - Models with commutative orthogonal block structure: a general condition for commutativity

AU - Santos, C.

AU - Nunes, C.

AU - Dias, C.

AU - Mexia, J. T.

N1 - This work was partially supported by national founds of FCT-Foundation for Science and Technology under UID/MAT/00297/2019 and UID/MAT/00212/2019.

PY - 2020

Y1 - 2020

N2 - A linear mixed model whose variance-covariance matrix is a linear combination of known pairwise orthogonal projection matrices that add to the identity matrix, is a model with orthogonal block structure (OBS). OBS have estimators with good behavior for estimable vectors and variance components, moreover it may be interesting that the least squares estimators give the best linear unbiased estimators, for estimable vectors. We can achieve it, requiring commutativity between the orthogonal projection matrix, on the space spanned by the mean vector, and the orthogonal projection matrices involved in the expression of the variance-covariance matrix. This commutativity condition defines a more restrict class of OBS, named COBS (model with commutative orthogonal block structure). With this work we aim to present a commutativity condition, resorting to a special class of matrices, named U-matrices.

AB - A linear mixed model whose variance-covariance matrix is a linear combination of known pairwise orthogonal projection matrices that add to the identity matrix, is a model with orthogonal block structure (OBS). OBS have estimators with good behavior for estimable vectors and variance components, moreover it may be interesting that the least squares estimators give the best linear unbiased estimators, for estimable vectors. We can achieve it, requiring commutativity between the orthogonal projection matrix, on the space spanned by the mean vector, and the orthogonal projection matrices involved in the expression of the variance-covariance matrix. This commutativity condition defines a more restrict class of OBS, named COBS (model with commutative orthogonal block structure). With this work we aim to present a commutativity condition, resorting to a special class of matrices, named U-matrices.

U2 - 10.1080/02664763.2020.1765322

DO - 10.1080/02664763.2020.1765322

M3 - Article

SN - 0266-4763

VL - 47

SP - 2421

EP - 2430

JO - Journal of Applied Statistics

JF - Journal of Applied Statistics

ER -