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Bayesian estimation of regression parameters in elliptical measurement error models

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  • Vidal, Ignacio
  • Bolfarini, Heleno

Abstract

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.

Suggested Citation

  • Vidal, Ignacio & Bolfarini, Heleno, 2011. "Bayesian estimation of regression parameters in elliptical measurement error models," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1398-1406, September.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:9:p:1398-1406
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    References listed on IDEAS

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    1. Vidal, Ignacio & Arellano-Valle, Reinaldo B., 2010. "Bayesian inference for dependent elliptical measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2587-2597, November.
    2. Bolfarine, Heleno & Arellano-Valle, Reinaldo B., 1998. "Weak nondifferential measurement error models," Statistics & Probability Letters, Elsevier, vol. 40(3), pages 279-287, October.
    3. Hobert, J. P. & Robert, C. P. & Goutis, C., 1997. "Connectedness conditions for the convergence of the Gibbs sampler," Statistics & Probability Letters, Elsevier, vol. 33(3), pages 235-240, May.
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