On misspecification of the dispersion matrix in mixed linear models |
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Authors: | Jian-Ying Rong Xu-Qing Liu |
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Institution: | (1) Department of Statistics and Mathematics Applied to Economics, University of Pisa, Via Ridolfi, 10, 50126 Pisa, Italy |
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Abstract: | The general mixed linear model can be written y = Xβ + Zu + e, where β is a vector of fixed effects, u is a vector of random effects and e is a vector of random errors. In this note, we mainly aim at investigating the general necessary and sufficient conditions
under which the best linear unbiased estimator for
\varvec r(\varvec l, \varvec m) = \varvec l\varvec ¢\varvec b+\varvec m\varvec ¢\varvec u{\varvec \varrho}({\varvec l}, {\varvec m}) = {\varvec l}{\varvec '}{\varvec \beta}+{\varvec m}{\varvec '}{\varvec u} is also optimal under the misspecified model. In addition, we offer approximate conclusions in some special situations including
a random regression model. |
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