ASYMPTOTIC NORMALITY AND VALID INFERENCE FOR GAUSSIAN VARIATIONAL APPROXIMATION

作者：Hall Peter^*; Tung Pham; Wand M P; Wang S S J

来源：Annals of Statistics, 2011, 39(5): 2502-2532.

DOI：10.1214/11-AOS908

• Generalized linear mixed models
• longitudinal data analysis
• maximum likelihood estimation
• Poisson mixed models

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.

• 出版日期2011-10