REML estimation: Asymptotic behavior and related topics

• 成果类型: Article
• 署名作者: Jiang, JM
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 255-286
• 关键词: variance-components; quadratic-forms; mixed model; likelihood; statistics

摘要

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.