REML ESTIMATION - ASYMPTOTIC-BEHAVIOR AND RELATED TOPICS

The restricted maximum likelihood (REML) estimates of dispersion param eters (variance components) in a general (non-normal) mixed model are defined as solutions of the REML equations. In this paper, we show the REML estimates are consistent if the model is asymptotically identifi able and infinitely informative under the (location) invariant class, and are asymptotically normal (A.N.) if in addition the model is asymp totically nondegenerate. The result does not require normality or boun dedness of the rank p of design matrix of fixed effects. Moreover, we give a necessary and sufficient condition for asymptotic normality of Gaussian maximum likelihood estimates (MLE) in non-normal cases. As an application, we show for all unconfounded balanced mixed models of th e analysis of variance the REML (ANOVA) estimates are consistent; and are also A.N. provided the models are nondegenerate; the MLE are consi stent (A.N.) if and only if certain constraints on p are satisfied.