TY - JOUR
T1 - Free-coordinate estimation for doubly multivariate data
AU - Kozioł, Arkadiusz
AU - Roy, Anuradha
AU - Zmyślony, Roman
AU - Leiva, Ricardo
AU - Fonseca, Miguel
N1 - info:eu-repo/grantAgreement/FCT/5876/147204/PT#
PY - 2018/6/15
Y1 - 2018/6/15
N2 - The article addresses the best unbiased estimators of the block compound symmetric covariance structure for m−variate observations with equal mean vector over u sites under the assumption of multivariate quasi-normality. The free-coordinate approach is used to prove that the quadratic estimation of covariance parameters is equivalent to linear estimation with a properly defined inner product in the space of symmetric matrices. Without assumption of normality but quasi-normality, meaning that up to fourth moments are the same as in the normal case, the estimators are best linear and best quadratic for mean and covariance parameters, respectively. Finally, strong consistency is proven. The properties of the estimators in the proposed model are compared against a similar model available in the literature. An application of the proposed approach to a clinical study data is presented.
AB - The article addresses the best unbiased estimators of the block compound symmetric covariance structure for m−variate observations with equal mean vector over u sites under the assumption of multivariate quasi-normality. The free-coordinate approach is used to prove that the quadratic estimation of covariance parameters is equivalent to linear estimation with a properly defined inner product in the space of symmetric matrices. Without assumption of normality but quasi-normality, meaning that up to fourth moments are the same as in the normal case, the estimators are best linear and best quadratic for mean and covariance parameters, respectively. Finally, strong consistency is proven. The properties of the estimators in the proposed model are compared against a similar model available in the literature. An application of the proposed approach to a clinical study data is presented.
KW - Best unbiased estimator
KW - Block compound symmetric covariance structure
KW - Coordinate free approach
KW - Doubly multivariate data
KW - Structured mean vector
UR - http://www.scopus.com/inward/record.url?scp=85042692006&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2018.02.019
DO - 10.1016/j.laa.2018.02.019
M3 - Article
AN - SCOPUS:85042692006
VL - 547
SP - 217
EP - 239
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
SN - 0024-3795
ER -