Abstract
The orthogonal complement likelihood junction is used to obtain the maximum likelihood estimates of the variance and covariance components. It is shown that these estimates are identical with Helmert's estimates and\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\Sigma } = E(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{e} \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{e} ')\) is a solution to maximize the orthogonal complement likelihood function. An approximate iterated method which leads to the maximum likelihood estimates is given. It is an extension of Förstner's iterated method.
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Ziqiang, O. Estimation of variance and covariance components. Bull. Geodesique 63, 139–148 (1989). https://doi.org/10.1007/BF02519147
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DOI: https://doi.org/10.1007/BF02519147