Bayesian bootstrap credible sets for multidimensional mean functional

Abstract

This paper shows that the Bayesian bootstrap (BB) distribution of a multidimensional mean functional based on i.i.d. observations has a strongly unimodal Lebesgue density provided the convex hull of the data has a nonempty interior. This result is then used to construct the finite sample BB credible sets. The influence of an outlier on these credible sets is studied in detail and a comparison is made with the empirical likelihood ratio confidence sets in this context.