Semiparametric Bayesian inference on generalized linear measurement error models

作者：Tang, Nian-Sheng^*; Li, De-Wang; Tang, An-Min

来源：Statistical Papers, 2017, 58(4): 1091-1113.

DOI：10.1007/s00362-016-0739-x

• Cook's distance
• Dirichlet process prior
• Generalized linear models
• Kullback-Leibler divergence
• Measurement error models

The classical assumption in generalized linear measurement error models (GLMEMs) is that measurement errors (MEs) for covariates are distributed as a fully parametric distribution such as the multivariate normal distribution. This paper uses a centered Dirichlet process mixture model to relax the fully parametric distributional assumption of MEs, and develops a semiparametric Bayesian approach to simultaneously obtain Bayesian estimations of parameters and covariates subject to MEs by combining the stick-breaking prior and the Gibbs sampler together with the Metropolis-Hastings algorithm. Two Bayesian case-deletion diagnostics are proposed to identify influential observations in GLMEMs via the Kullback-Leibler divergence and Cook's distance. Computationally feasible formulae for evaluating Bayesian case-deletion diagnostics are presented. Several simulation studies and a real example are used to illustrate our proposed methodologies.

• 出版日期2017-12
• 单位云南大学