Semiparametric Bayesian measurement error modeling |
| |
Authors: | María P Casanova Alexis Peña |
| |
Institution: | a Departamento de Estadística, Facultad de Ciencias Físicas y Matemáticas, Universidad of Concepción, Chile b Departamento de Estadística, Facultad de Matemática, Pontificia Universidad Católica de Chile, Chile c Instituto de Matemática e Estatística, Universidade de São Paulo, Brazil d Departamento de Matemática y Ciencia de la Computación, Facultad de Ciencia, Universidad de Santiago de Chile, Chile |
| |
Abstract: | 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. |
| |
Keywords: | 62A15 62J05 |
本文献已被 ScienceDirect 等数据库收录! |
|