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Robust Bayesian Inference on Scale Parameters

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  • Fernández, Carmen
  • Osiewalski, Jacek
  • Steel, Mark F. J.

Abstract

We represent random vectors Z that take values in n-{0} as Z=RY, where R is a positive random variable and Y takes values in an (n-1)-dimensional space . By fixing the distribution of either R or Y, while imposing independence between them, different classes of distributions on n can be generated. As examples, the spherical, lq-spherical, [upsilon]-spherical and anisotropic classes can be interpreted in this unifying framework. We present a robust Bayesian analysis on a scale parameter in the pure scale model and in the regression model. In particular, we consider robustness of posterior inference on the scale parameter when the sampling distribution ranges over classes related to those mentioned above. Some links between Bayesian and sampling-theory results are also highlighted.

Suggested Citation

  • Fernández, Carmen & Osiewalski, Jacek & Steel, Mark F. J., 2001. "Robust Bayesian Inference on Scale Parameters," Journal of Multivariate Analysis, Elsevier, vol. 77(1), pages 54-72, April.
    • Handle: RePEc:eee:jmvana:v:77:y:2001:i:1:p:54-72
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    References listed on IDEAS

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    1. Osiewalski, Jacek & Steel, Mark F.J., 1992. "Robust Bayesian inference in Iq-Spherical models," UC3M Working papers. Economics 2843, Universidad Carlos III de Madrid. Departamento de Economía.
    2. Fang, Kai-Tai & Li, Runze, 1999. "Bayesian Statistical Inference on Elliptical Matrix Distributions," Journal of Multivariate Analysis, Elsevier, vol. 70(1), pages 66-85, July.
    3. Fernandez, C & Osiewalski, J & Steel, M-F-J, 1996. "Classical and Bayesian Inference Robustness in Multivariate Regression models," Papers 9602, Catholique de Louvain - Institut de statistique.
    4. Fang, Kai-Tai & Bentler, P. M., 1991. "A largest characterization of spherical and related distributions," Statistics & Probability Letters, Elsevier, vol. 11(2), pages 107-110, February.
    5. Gupta, A. K. & Song, D., 1997. "Characterization ofp-Generalized Normality," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 61-71, January.
    6. Akimichi Takemura & Satoshi Kuriki, 1996. "A proof of independent Bartlett correctability of nested likelihood ratio tests," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(4), pages 603-620, December.
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