Gibbs posterior inference on multivariate quantiles

Bayesian and other likelihood-based methods require specification of a statistical model may not be fully satisfactory for inference on quantities, such as quantiles, that are naturally defined parameters. In this paper, we construct direct model-free Gibbs posterior distribution multivariate quantiles. Being means inferences drawn from the subject to misspecification bias, being no priors or marginalization over nuisance parameters required. We show here enjoys root-n convergence rate Bernstein–von Mises property, i.e., large n, can approximated by Gaussian. Moreover, present numerical results showing validity efficiency credible sets derived suitably scaled posterior.