ASYMPTOTIC NORMALITY AND VALID INFERENCE FOR GAUSSIAN VARIATIONAL APPROXIMATION

被引：31

作者：

Hall, Peter ^{[1
]}

Tung Pham ^{[2
]}

Wand, M. P. ^{[3
]}

Wang, S. S. J. ^{[2
]}

机构：

[1] Univ Melbourne, Dept Math & Stat, Melbourne, Vic 3000, Australia

[2] Univ Wollongong, Sch Math & Appl Stat, Ctr Stat & Survey Methodol, Wollongong, NSW 2522, Australia

[3] Univ Technol Sydney, Sch Math Sci, Sydney, NSW 2007, Australia

来源：

ANNALS OF STATISTICS | 2011年 / 39卷 / 05期

基金：

澳大利亚研究理事会;

关键词：

Generalized linear mixed models; longitudinal data analysis; maximum likelihood estimation; Poisson mixed models; BAYES;

D O I：

10.1214/11-AOS908

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：2502 / 2532

页数：31

共 18 条

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