OPTIMAL QUADRATIC UNBIASED ESTIMATION FOR MODELS WITH LINEAR TOEPLITZ COVARIANCE STRUCTURE

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. F...

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Bibliographic Details
Published in:Statistics (Berlin, DDR) DDR), 2003-03, Vol.37 (2), p.85-99
Main Authors: MARIN, JEAN-MICHEL, DHORNE, THIERRY
Format: Article
Language:English
Subjects:
Mathematics
Mivque
Optimal Linear Estimation
Special Jordan Algebras
Statistics
Toeplitz Covariance
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Summary: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.
ISSN:0233-1888
1029-4910
DOI:10.1080/02331880290015468