A BAYESIAN APPROACH TO ENVELOPE QUANTILE REGRESSION

The enveloping approach employs sufficient dimension-reduction tech- niques to gain estimation efficiency, and has been used in several multivariate anal- ysis contexts. However, its Bayesian development has been sparse, and the only Bayesian envelope construction is in the context of a linear regression. In this pa- per, we propose a Bayesian envelope approach to a quantile regression, using a gen- eral framework that may potentially aid enveloping in other contexts as well. The proposed approach is also extended to accommodate censored data. Data augmen- tation Markov chain Monte Carlo algorithms are derived for approximate sampling from the posterior distributions. Simulations and data examples are included for illustration.