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October 2011 Asymptotic normality and valid inference for Gaussian variational approximation
Peter Hall, Tung Pham, M. P. Wand, S. S. J. Wang
Ann. Statist. 39(5): 2502-2532 (October 2011). DOI: 10.1214/11-AOS908


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.


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Peter Hall. Tung Pham. M. P. Wand. S. S. J. Wang. "Asymptotic normality and valid inference for Gaussian variational approximation." Ann. Statist. 39 (5) 2502 - 2532, October 2011.


Published: October 2011
First available in Project Euclid: 30 November 2011

zbMATH: 1231.62029
MathSciNet: MR2906876
Digital Object Identifier: 10.1214/11-AOS908

Primary: 62F12
Secondary: 62F25

Keywords: generalized linear mixed models , longitudinal data analysis , maximum likelihood estimation , Poisson mixed models

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 5 • October 2011
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