Centre for Statistical & Survey Methodology Working Paper Series

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We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a singlepredictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical properties of a variational approximation method. Moreover, they give rise to asymptotically valid statistical inference. A simulation study demonstrates that Gaussian variational approximate confidence intervals possess good to excellent coverage properties, and with precision similar to their exact likelihood counterparts.