Bayesian Bootstrap Credible Sets for the Multivariate Mean

Abstract


The purpose of this talk is to show how we may obtain a Bayesian set estimate for the multivariate mean. First we shall introduce the Bayesian bootstrap distribution as a nonparametric tool in this context. Then we shall see that the Bayesian bootstrap (BB) distribution of the multivariate mean 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. Then 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.

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