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Optimal quadratic unbiased estimation for models with linear Toeplitz covariance structure

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Dewey
Probabilités et mathématiques appliquées
Sujet
Special Jordan Algebras; Mivque; Toeplitz Covariance; Optimal Linear Estimation
Journal issue
Statistics. A journal of Theoretical and Applied Statistics
Volume
37
Number
2
Publication date
08-2010
Article pages
85-99
Publisher
Taylor & Francis
DOI
http://dx.doi.org/10.1080/02331880290015468
URI
https://basepub.dauphine.fr/handle/123456789/17464
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Marin, Jean-Michel
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Dhorne, Thierry
81533 Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (UMR 3192) [Lab-STICC]
Type
Article accepté pour publication ou publié
Abstract (EN)
This paper deals with the problem of quadratic unbiased estimation for models with linear Toeplitz covariance structure. These serial covariance models are very useful to modelize time or spatial correlations by means of linear models. Optimality and local optimality is examined in different ways. For the nested Toeplitz models, it is shown that there does not exist a Uniformly Minimum Variance Quadratic Unbiased Estimator for at least one linear combination of covariance parameters. Moreover, empirical unbiased estimators are identified as Locally Minimum Variance Quadratic Unbiased Estimators for a particular choice on covariance parameters corresponding to the case where the covariance matrix of the observed random vector is proportional to the identity matrix. The complete Toeplitz-circulant model is also studied. For this model, the existence of a Uniformly Minimum Variance Quadratic Unbiased Estimator for each covariance parameter is proved.

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