Bayesian Empirical Likelihood for Quantile Regression: A Bayesian Approach to Efficiently Model Multiple Tail Quantiles

• Activity Number: 545
• Type: Invited
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Yunwen Yang*+ and Xuming He
• Companies: Drexel University and University of Michigan
• Keywords: quantile regression ; tail quantiles ; Bayesian ; statistical downscaling

Abstract

In climate studies, quantities corresponding to extreme climate events are of particular interest. Quantile regression, which directly target at selected percentile levels (e.g., tail quantiles), is a flexible nonparametric tool to model the unusual climate events. Usually, quantile regression estimation is carried out at one percentile level at a time, and the resulting estimates tend to have high variability in the data sparse areas (e.g., the upper or lower tails of the conditional distributions). In this talk, we introduce the Bayesian empirical likelihood approach (BEL) to quantile regression, which enables us to explore certain commonality across quantiles through informative priors. The BEL approach facilitates an efficient way of joint estimation of several quantiles, leading to more efficient quantile estimation, especially at tail quantiles. The utilization of informative priors also enables quantile regression to model spatially correlated climate data in a flexible manner. We show that the posterior-based inference for BEL is asymptotically valid, and demonstrate both theoretically and empirically how the BEL approach improves efficiency over the usual quantile regres