Asymptotic normality and valid inference for Gaussian variational approximation
Peter Hall, Tung Pham, M. P. Wand, S. S. J. Wang
The Annals of Statistics · 2011 · Volume 39 · Issue 5
Abstract
We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor 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 have a similar precision to their exact likelihood counterparts.
Keywords
62F12, 62F25, generalized linear mixed models, longitudinal data analysis, maximum likelihood estimation, Poisson mixed models
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