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Biometrika 1994 81(3):588-594; doi:10.1093/biomet/81.3.588
© 1994 by Biometrika Trust
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MISCELLANEA

The continuous multivariate location-scale model revisited: A tale of robustness

CARMEN FERNÁNDEZ1, JACEK OSIEWALSKI2 and MARK F. J. STEEL3

1 Department of Mathematics, Universidad Autónoma 28049 Madrid, Spain
2 Department of Econometrics, Academy of Economics 31-510 Kraków, Poland
3 CentER nd Deprtment of Econometrics, Tilburg University 5000 LE Tilburg, The Netherlands

Received for publication 1 November 1993. Revision received 1 February 1994.
  Abstract

We consider the location-scale family of all multivariate continuous sampling distributions. Any model from the subclass induced by fixing a particular distribution on the unit sphere, combined with a standard improper prior on the scale parameter, will lead to the same inference on location and observables. This finding sheds light on many robustness results in less general models and its implications are illustrated in a number of examples.

Key Words: Bayesian inference • Cardioid distribution • Model robustness • Multivariate distribution theory • Nuisance parameter


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