Asymptotic normality and valid inference for Gaussian variational approximation

Hall, P; Pham, T; Wand, MP; Wang, SSJ

Asymptotic normality and valid inference for Gaussian variational approximation

Hall, P Pham, T Wand, MP Wang, SSJ

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Publisher:: Institute of Mathematical Statistics (IMS)
Publication Type:: Journal Article
Citation:: Annals of Statistics, 2011, 39 (5), pp. 2502 - 2532
Issue Date:: 2011

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Field	Value	Language
dc.contributor.author	Hall, P	en_US
dc.contributor.author	Pham, T	en_US
dc.contributor.author	Wand, MP	en_US
dc.contributor.author	Wang, SSJ	en_US
dc.date.issued	2011	en_US
dc.identifier.citation	Annals of Statistics, 2011, 39 (5), pp. 2502 - 2532	en_US
dc.identifier.issn	0090-5364	en_US
dc.identifier.uri	http://hdl.handle.net/10453/41194
dc.description.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.	en_US
dc.publisher	Institute of Mathematical Statistics (IMS)	en_US
dc.relation.ispartof	Annals of Statistics	en_US
dc.relation.isbasedon	10.1214/11-AOS908	en_US
dc.subject.classification	Statistics & Probability	en_US
dc.title	Asymptotic normality and valid inference for Gaussian variational approximation	en_US
dc.type	Journal Article
utslib.citation.volume	5	en_US
utslib.citation.volume	39	en_US
utslib.for	0104 Statistics	en_US
utslib.for	1403 Econometrics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	open_access
pubs.declined	2016-01-14T11:44:49.692+1100
pubs.consider-herdc	true	en_US
pubs.deleted	2016-01-14T11:44:49.692+1100
pubs.issue	5	en_US
pubs.publication-status	Published	en_US
pubs.volume	39	en_US

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.

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http://hdl.handle.net/10453/41194