Semiparametric Bayesian measurement error modeling

JOURNAL OF MULTIVARIATE ANALYSIS

卷:101

Article

Casanova, Maria P.²  Iglesias, Pilar³  Bolfarine, Heleno⁴  Salinas, Victor H.¹  Pena, Alexis³ 

[1] Univ Santiago Chile, Fac Ciencia, Dept Matemat & Ciencia Computac, Santiago, Chile

[2] Univ Concepcion, Fac Ciencias Fis & Matemat, Dept Estadist, Concepcion, Chile

[3] Pontificia Univ Catolica Chile, Fac Matemat, Dept Estadist, Santiago, Chile

[4] Univ Sao Paulo, Inst Matemat & Estatist, BR-05508 Sao Paulo, Brazil

关键词: Classical measurement error model;    Hierarchical elliptical model;    Posterior distribution;    Dirichlet process;    Gibbs sampling;   

DOI  :  10.1016/j.jmva.2009.11.004

来源: Elsevier

【 摘 要 】

This work presents a Bayesian semiparametric approach for dealing with regression models where the covariate is measured with error. Given that (1) the error normality assumption is very restrictive, and (2) assuming a specific elliptical distribution for errors (Student-t for example), may be somewhat presumptuous; there is need for more flexible methods, in terms of assuming only symmetry of errors (admitting unknown kurtosis). In this sense, the main advantage of this extended Bayesian approach is the possibility of considering generalizations of the elliptical family of models by using Dirichlet process priors in dependent and independent situations. Conditional posterior distributions are implemented, allowing the use of Markov Chain Monte Carlo (MCMC), to generate the posterior distributions. An interesting result shown is that the Dirichlet process prior is not updated in the case of the dependent elliptical model. Furthermore, an analysis of a real data set is reported to illustrate the usefulness of our approach, in dealing with outliers. Finally, semiparametric proposed models and parametric normal model are compared, graphically with the posterior distribution density of the coefficients. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free