Semiparametric Bayesian inference on generalized linear measurement error models

• Published in: Statistical papers (Berlin, Germany) Vol. 58; no. 4; pp. 1091 - 1113
• Main Authors: Tang, Nian-Sheng, Li, De-Wang, Tang, An-Min
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2017; Springer Nature B.V
• Subjects: Bayesian analysis; Computer simulation; Deletion; Dirichlet problem; Divergence; Economic models; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Error analysis; Feasibility studies; Finance; Insurance; Management; Mathematics and Statistics; Normal distribution; Operations Research/Decision Theory; Parameter estimation; Probability Theory and Stochastic Processes; Regular Article; Statistical inference; Statistics; Statistics for Business; Measurement error models; Cook’s distance; Kullback–Leibler divergence; Generalized linear models; Dirichlet process prior
• ISSN: 0932-5026; 1613-9798
• DOI: 10.1007/s00362-016-0739-x

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.