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Semiparametric Bayesian inference on generalized linear measurement error models

Author

Listed:
  • Nian-Sheng Tang

    (Yunnan University)

  • De-Wang Li

    (Yunnan University)

  • An-Min Tang

    (Yunnan University)

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.

Suggested Citation

  • Nian-Sheng Tang & De-Wang Li & An-Min Tang, 2017. "Semiparametric Bayesian inference on generalized linear measurement error models," Statistical Papers, Springer, vol. 58(4), pages 1091-1113, December.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:4:d:10.1007_s00362-016-0739-x
    DOI: 10.1007/s00362-016-0739-x
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    References listed on IDEAS

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