Asymptotic Theory for Restricted Maximum Likelihood Estimators in Generalized Linear Mixed Models

2026-09-12

AI Summary

本文解决了广义线性混合模型中限制最大似然估计量的渐近理论问题，通过证明当群集数量和大小趋于无穷时估计量的渐近正态性。

Abstract

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.

Problem

• restricted maximum likelihood
• generalized linear mixed models
• asymptotic theory

Innovation

• Asymptotic Theory
• Restricted Maximum Likelihood (REML)
• Generalized Linear Mixed Models (GLMMs)
• Block-Diagonal Covariance Structure
• Bias-Correction