REML estimation: asymptotic behavior and related topics
Jiming Jiang
Source: Ann. Statist. Volume 24, Number 1 (1996), 255-286.
Abstract
The restricted maximum likelihood (REML) estimates of dispersion parameters (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 identifiable and infinitely informative under the (location) invariant class, and are asymptotically normal (A.N.) if in addition the model is asymptotically nondegenerate. The result does not require normality or boundedness 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 the analysis of variance the REML (ANOVA) estimates are consistent; and are also A.N. provided the models are nondegenerate; the MLE are consistent (A.N.) if and only if certain constraints on p are satisfied.
Primary Subjects: 62F12
Keywords: Mixed models; restricted maximum likelihood; MLE; ANOVA; consistency; asymptotic normality
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aos/1033066209
Mathematical Reviews number (MathSciNet):
MR1389890
Digital Object Identifier: doi:10.1214/aos/1033066209
Zentralblatt MATH identifier:
0853.62022
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