The use of generalized inverses in restricted maximum likelihood |
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Authors: | FJ Henk Don |
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Institution: | Central Planning Bureau The Hague, Netherlands |
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Abstract: | 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 Aitchison and Silvey 1]. We use the approach recently developed by Heijmans and Magnus 13, 14] to allow for non-i.i.d. observations. A nonlinear seemingly unrelated regressions model with possibly singular covariance matrix and linear restrictions (NLSURSR) is analyzed, and the linear expenditure system (LES) is discussed as a special case. |
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