The Linear Model with Restricted Explanatory Variables

Linear models with linear equality constraints on the coefficients are translated into models with a singular design matrix and a nonsingular disturbances covariance matrix in order to deduce general conditions for estimability and testability. Simplifications of the recursive least squares algorith...

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Bibliographic Details
Published in:International statistical review 1991-12, Vol.59 (3), p.279-285
Main Author: Annibal Parracho Sant'Anna
Format: Article
Language:English
Subjects:
Covariance matrices
Estimators
Exact sciences and technology
Least squares
Linear models
Mathematics
Maximum likelihood estimators
Modeling
Null condition
Null set
Parametric models
Probability and statistics
Sciences and techniques of general use
Statistics
Uniqueness
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Summary:Linear models with linear equality constraints on the coefficients are translated into models with a singular design matrix and a nonsingular disturbances covariance matrix in order to deduce general conditions for estimability and testability. Simplifications of the recursive least squares algorithm for the singular case are discussed. /// Afin de trouver des conditions assurant que certains paramètres soient estimables et que certaines hypothèses soient testables, on transforme des modèles linéaires où les paramètres sont constraints par des équations linéaires en modèles dont la matrice de variables explicatives est singulière mais celle des covariances est non-singulière. On discute des simplifications de l'algorithme des moindres carrés itérés.
ISSN:0306-7734
1751-5823
DOI:10.2307/1403688