Wald consistency and the method of sieves in REML estimation

• 成果类型: Article
• 署名作者: Jiang, JM
• 署名单位: University System of Ohio; Case Western Reserve University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 1781-1803
• 关键词: variance-components

摘要

We prove that for all unconfounded balanced mixed models of the analysis of variance, estimates of variance components parameters that maximize the (restricted) Gaussian Likelihood are consistent and asymptotically normal-and this is true whether normality is assumed or not. For a general (nonnormal) mixed model, we show estimates of the variance components parameters that maximize the (restricted) Gaussian likelihood over a sequence of approximating parameter spaces (i.e., a sieve) constitute a consistent sequence of roots of the REML equations and the sequence is also asymptotically normal. The results do not require the rank p of the design matrix of fixed effects to be bounded. An example shows that, in some unbalanced cases, estimates that maximize the Gaussian likelihood over the full parameter space can be inconsistent, given the condition that ensures consistency of the sieve estimates.