Second Term Improvement to Generalised Linear Mixed Model Asymptotics
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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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