Bayesian analysis of the calibration problem under elliptical distributions

Abstract

In this paper we discuss calibration problems under dependent and independent elliptical family of distributions. In the dependent case, it is shown that the posterior distribution of the quantity of interest is robust with respect to the distributions in the elliptical family. In particular, the results obtained by Hoadley (1970. J. Amer. Statist. 65, 356-369) showing that the inverse estimator is a Bayes estimator under normal models with a Student-t prior also holds under the dependent elliptical family of distributions. In the independent case, the use of the elliptical family allows the consideration of models which provide protection against possible outliers in the data. The multivariate calibration problem is also considered, where some results given in Brown (1993. Measurement, Regression and Calibration. Oxford University Press, Oxford) are extended. Finally, the results of the paper are applied to a real data problem, showing that the Student-t model can be a valid alternative to normality. (C) 2000 Elsevier Science B.V. All rights reserved.

MSC: 62F15; 62F35; 62J05.