The use of generalized inverses in restricted maximum likelihood
type: Item
instance of: scholarly article
title: The use of generalized inverses in restricted maximum likelihood
zbMATH Open document ID: 0609.62081
DOI: 10.1016/0024-3795(85)90054-0
author: F. J. Henk Don
published in: Linear Algebra and its Applications
publication date: 1985-01-01T00:00:00Z
review text: The calculus of generalized inverses and related concepts in matrix algebra is applied to the general restricted maximum likelihood problem. Some new results on g-inverses, Kronecker products, and matrix differentials are presented. For the restricted maximum likelihood problem we obtain generalizations of the well-known results of \textit{J. Aitchison} and \textit{S. D. Silvey} [Ann. Math. Stat. 29, 813-828 (1958; Zbl 0092.367)]. We use the approach recently developed by \textit{R. D. H. Heijmans} and \textit{J. R. Magnus} [Asymptotic properties of maximum likelihood estimators in the nonlinear regression model when the errors are neither independent nor identically distributed. Rep. AE 20/82, Univ. Amsterdam (1982); On the asymptotic normality of the maximum likelihood estimator with dependent observations. Rep. AE 14/83, Univ. Amsterdam (1983)] to allow for non-i.i.d. observations. A nonlinear seemingly unrelated regressions model with possibly singular covariance matrix and linear restrictions is analyzed, and the linear expenditure system is discussed as a special case.
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62H10
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A69
Mathematics Subject Classification ID: 62P20
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 3986434
zbMATH Keywords: bordered information matrix
zbMATH Keywords: convergence in probability
zbMATH Keywords: generalized method of scoring
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: generalized inverses
zbMATH Keywords: general restricted maximum likelihood
zbMATH Keywords: Kronecker products
zbMATH Keywords: matrix differentials
zbMATH Keywords: nonlinear seemingly unrelated regressions model
zbMATH Keywords: singular covariance matrix
zbMATH Keywords: linear restrictions
zbMATH Keywords: linear expenditure system
MaRDI profile type: Publication
full work available at URL: 0024-3795(85)90054-0
OpenAlex ID: W2080535010
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description: scientific article; zbMATH DE number 3986434