Robust Bayesian inference on scale parameters

Author Info

• Carmen Fernandez
• Jacek Osiewalski
• M. F. J. Steel
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Abstract

We represent random variables $Z$ that take values in $\Re^n-\{0\}$ as $Z=RY$, where $R$ is a positive random variable and $Y$ takes values in an $(n-1)$-dimensional space $\cal Y$. By fixing the distribution of either $R$ or $Y$, while imposing independence between them, different classes of distributions on $\Re^n$ can be generated. As examples, the spherical, $l_q$-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.

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Bibliographic Info

Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 25.

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Handle: RePEc:edn:esedps:25

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1. 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.
2. Gupta, A. K. & Song, D., 1997. "Characterization ofp-Generalized Normality," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 61-71, January.
3. Steel, M.F.J., 1991. "Bayesian Inference in Time Series," Papers 9153, Tilburg - Center for Economic Research.
4. 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.
5. 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.
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