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arXiv · 2303.17855

Second Term Improvement to Generalised Linear Mixed Model Asymptotics

Luca Maestrini·Aishwarya Bhaskaran·Matt P. Wand
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Abstract

A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If $m$ denotes the number of groups and $n$ is the average within-group sample size then the asymptotic variances have orders $m^{-1}$ and $(mn)^{-1}$, depending on the parameter. We extend this theory to provide explicit forms of the $(mn)^{-1}$ second terms of the asymptotically harder-to-estimate parameters. Improved accuracy of studentised confidence intervals is one consequence of our theory.

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Luca Maestrini, Aishwarya Bhaskaran, Matt P. Wand. 2023-03-31. Second Term Improvement to Generalised Linear Mixed Model Asymptotics. https://arxiv.org/abs/2303.17855

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