Semiparametric Bayesian inference on generalized linear measurement error models

Nian-Sheng Tang (), Li De-Wang and An-Min Tang
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Nian-Sheng Tang: Yunnan University
Li De-Wang: Yunnan University
An-Min Tang: Yunnan University

Statistical Papers, 2017, vol. 58, issue 4, No 6, 1113 pages

Abstract: Abstract 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.

Keywords: Cook’s distance; Dirichlet process prior; Generalized linear models; Kullback–Leibler divergence; Measurement error models (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s00362-016-0739-x

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