The use of generalized inverses in restricted maximum likelihood (Q1086945)

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.