发表机构
School of Systems and Computing, University of New South Wales; UNSW Data Science Hub; School of Mathematics and Statistics, University of New South Wales（新南威尔士大学系统计算学院; 新南威尔士大学数据科学中心; 新南威尔士大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为广义线性混合模型中的限制最大似然估计建立了渐近正态性理论，在温和条件下证明了其偏差校正性质，并通过模拟和遗传数据验证。
AI 中文摘要
几十年来，为广义线性混合模型（GLMMs）中的限制最大似然（REML）估计量建立渐近理论一直是一个悬而未决的问题。在本文中，当簇数量和簇大小都趋于无穷时，我们建立了GLMMs中REML和最大似然（ML）估计量的渐近分布。在非常温和的条件下，仅要求随机效应具有有限矩假设而非正态性，并且不限制簇数量和簇大小发散相对速率，两个估计量都被证明具有显式的块对角协方差结构的渐近正态性，并建立了REML的偏差校正性质。模拟研究支持了渐近结果，遗传数据分析说明了该方法。
英文摘要
Developing an asymptotic theory for restricted maximum likelihood (REML) estimators in generalized linear mixed models (GLMMs) has remained an open problem for decades. In this paper, we establish the asymptotic distributions of the REML and maximum likelihood (ML) estimators for GLMMs when both the number of clusters and the cluster sizes tend to infinity. Under very mild conditions, requiring only finite-moment assumptions on the random effects rather than normality and imposing no restriction on the relative rates at which the number of clusters and the cluster sizes diverge, both estimators are proved to be asymptotically normal with an explicit block-diagonal covariance structure, and the bias-correction property of REML is established. Simulation studies support the asymptotic results, and a genetic data analysis illustrates the methodology.
CommentsMain text: 21 pages, 3 tables Supplementary: 80 pages, 14 tables
