Bayesian nonparametric tests for multivariate locations
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In this paper, we propose Bayesian non-parametric tests for one-sample and two-sample multivariate location problems. We model the underlying distributions using a Dirichlet process prior. For the one-sample problem, we compute a Bayesian credible set of the multivariate spatial median and accept the null hypothesis if the credible set contains the null value. For the two-sample problem, we form a credible set for the difference of the spatial medians of the two samples and we accept the null hypothesis of equality if the credible set contains zero. We derive the local asymptotic power of the tests under shrinking alternatives, and also present a simulation study to compare the finite-sample performance of our testing procedures with existing parametric and non-parametric tests.
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