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On misspecification of the dispersion matrix in mixed linear models. (English) Zbl 1247.62140

Summary: The general mixed linear model can be written \(y= X\beta+{Zu}+e\), where \(\beta\) 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 \(\rho(l,m)=l'\beta+ m'u\) is also optimal under a misspecified model. In addition, we offer approximate conclusions in some special situations, including a random regression model.

MSC:

62H12 Estimation in multivariate analysis
62J05 Linear regression; mixed models
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