Bayesian estimation of regression parameters in elliptical measurement error models

  • Vidal I
  • Bolfarini H
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The main object of this paper is to discuss the Bayes estimation of the
regression coefficients in the elliptically distributed simple
regression model with measurement errors. The posterior distribution for
the line parameters is obtained in a closed form, considering the
following: the ratio of the error variances is known, informative prior
distribution for the error variance, and non-informative prior
distributions for the regression coefficients and for the incidental
parameters. We proved that the posterior distribution of the regression
coefficients has at most two real modes. Situations with a single mode
are more likely than those with two modes, especially in large samples.
The precision of the modal estimators is studied by deriving the Hessian
matrix, which although complicated can be computed numerically. The
posterior mean is estimated by using the Gibbs sampling algorithm and
approximations by normal distributions. The results are applied to a
real data set and connections with results in the literature are
reported. (C) 2011 Elsevier B.V. All rights reserved.

Author-supplied keywords

  • Bayesian inference; Dependent measurement error mo

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  • Ignacio Vidal

  • Heleno Bolfarini

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