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February 1996 REML estimation: asymptotic behavior and related topics
Jiming Jiang
Ann. Statist. 24(1): 255-286 (February 1996). DOI: 10.1214/aos/1033066209


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.


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Jiming Jiang. "REML estimation: asymptotic behavior and related topics." Ann. Statist. 24 (1) 255 - 286, February 1996.


Published: February 1996
First available in Project Euclid: 26 September 2002

zbMATH: 0853.62022
MathSciNet: MR1389890
Digital Object Identifier: 10.1214/aos/1033066209

Primary: 62F12

Keywords: ANOVA , asymptotic normality , consistency , mixed models , MLE , restricted maximum likelihood

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 1 • February 1996
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