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Bayesian inference for dependent elliptical measurement error models

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  • Vidal, Ignacio
  • Arellano-Valle, Reinaldo B.

Abstract

In this article we provide a Bayesian analysis for dependent elliptical measurement error models considering nondifferential and differential errors. In both cases we compute posterior distributions for structural parameters by using squared radial prior distributions for the precision parameters. The main result is that the posterior distribution of location parameters, for specific priors, is invariant with respect to changes in the generator function, in agreement with previous results obtained in the literature under different assumptions. Finally, although the results obtained are valid for any elliptical distribution for the error term, we illustrate those results by using the student-t distribution and a real data set.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:10:p:2587-2597
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    References listed on IDEAS

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    1. Arellano-Valle, R.B. & Ozan, S. & Bolfarine, H. & Lachos, V.H., 2005. "Skew normal measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 265-281, October.
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    5. Bolfarine, Heleno & Arellano-Valle, Reinaldo B., 1998. "Weak nondifferential measurement error models," Statistics & Probability Letters, Elsevier, vol. 40(3), pages 279-287, October.
    6. Manuel Galea & Heleno Bolfarine & Filidor Vilcalabra, 2002. "Influence diagnostics for the structural errors-in-variables model under the Student-t distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(8), pages 1191-1204.
    7. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    8. Arellano-Valle, R.B. & del Pino, G. & Iglesias, P., 2006. "Bayesian inference in spherical linear models: robustness and conjugate analysis," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 179-197, January.
    9. Fernando A. Quintana & Pilar L. Iglesias & Heleno Bolfarine, 2005. "Bayesian Identification Of Outliers And Change-Points In Measurement Error Models," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 8(04), pages 433-449.
    10. Myung Geun Kim, 2000. "Outliers and influential observations in the structural errors-in-variables model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(4), pages 451-460.
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    Cited by:

    1. 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.

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