# Orthogonal models: Algebraic structure and explicit estimators for estimable vectors

Artur Pereira; Miguel Fonseca; João Tiago Mexia

Discussiones Mathematicae Probability and Statistics (2015)

- Volume: 35, Issue: 1-2, page 29-44
- ISSN: 1509-9423

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topArtur Pereira, Miguel Fonseca, and João Tiago Mexia. "Orthogonal models: Algebraic structure and explicit estimators for estimable vectors." Discussiones Mathematicae Probability and Statistics 35.1-2 (2015): 29-44. <http://eudml.org/doc/276480>.

@article{ArturPereira2015,

abstract = {We study the algebraic structure of orthogonal models thus of mixed models whose variance covariance matrices are all positive semi definite, linear combinations of known pairwise orthogonal projection matrices, POOPM, and whose least square estimators, LSE, of estimable vectors are best linear unbiased estimator, BLUE, whatever the variance components, so they are uniformly BLUE, UBLUE. From the results of the algebraic structure we will get explicit expression for the LSE of these models.},

author = {Artur Pereira, Miguel Fonseca, João Tiago Mexia},

journal = {Discussiones Mathematicae Probability and Statistics},

keywords = {linear models; mixed models; inference; orthogonal models; UBLUE},

language = {eng},

number = {1-2},

pages = {29-44},

title = {Orthogonal models: Algebraic structure and explicit estimators for estimable vectors},

url = {http://eudml.org/doc/276480},

volume = {35},

year = {2015},

}

TY - JOUR

AU - Artur Pereira

AU - Miguel Fonseca

AU - João Tiago Mexia

TI - Orthogonal models: Algebraic structure and explicit estimators for estimable vectors

JO - Discussiones Mathematicae Probability and Statistics

PY - 2015

VL - 35

IS - 1-2

SP - 29

EP - 44

AB - We study the algebraic structure of orthogonal models thus of mixed models whose variance covariance matrices are all positive semi definite, linear combinations of known pairwise orthogonal projection matrices, POOPM, and whose least square estimators, LSE, of estimable vectors are best linear unbiased estimator, BLUE, whatever the variance components, so they are uniformly BLUE, UBLUE. From the results of the algebraic structure we will get explicit expression for the LSE of these models.

LA - eng

KW - linear models; mixed models; inference; orthogonal models; UBLUE

UR - http://eudml.org/doc/276480

ER -

## References

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