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Linear Toeplitz covariance structure models with optimal estimators of variance components

Marin, Jean-Michel; Dhorne, Thierry, Linear Toeplitz covariance structure models with optimal estimators of variance components, Linear Algebra and its Applications;0024-3795, 354, 1-3, p. 195-212. 10.1016/S0024-3795(02)00325-7

Type
Article accepté pour publication ou publié
Journal name
Linear Algebra and its Applications;0024-3795
Volume
354
Number
1-3
Publisher
Elsevier
Pages
195-212
Publication identifier
Metadata
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Author(s)
Marin, Jean-Michel cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Dhorne, Thierry
Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (UMR 3192) [Lab-STICC]
Abstract (EN)
This paper deals with the problem of optimal quadratic unbiased estimation for statistical models with linear Toeplitz covariance structure. The main result is a necessary and sufficient condition for these models to have an optimal unbiased estimator for any linear combination of variance components. This result is obtained by means of special Jordan algebras which are a powerful tool to characterize optimality in quadratic unbiased estimation.
Subjects / Keywords
Circulant and skewcirculant matrices; Toeplitz matrices; Special Jordan algebras; Quadratic unbiased estimation