The Continuous Multivariate Location-Scale Model Revisited: A Tale of Robustness

Abstract

SummaryWe considcr the location-scale faniily of all nrultivariate continuous sampling distributions. Any tnodel from t.he subclass induced by fixing a particular distribution on the unit. sphc~re,, combine~d with a standard improper prior on the scale paranteter, will lead to the satne inícrcure ou location ancí observ~ables. This finding sheds light on many robustness rosults in lcss general rnodels and its implications are illustrated in a number of examples.