Special Colloquium
Yunwen Yang
UIUC
Bayesian Empirical Likelihood for Quantile Regression
Abstract: Quantile regression extends the familiar notations of sorting and ranking in the
elementary one-sample context to a much broader class of statistical models. Instead of focusing on the conditional mean based on the least squares regression, quantile regression provides more comprehensive information on how the covariates influence the entire distributions of the response variables. 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 distributions). In this talk, we consider a Bayesian empirical likelihood approach (BEL) to quantile regression. By using the empirical likelihood as a working likelihood, the BEL approach can explore various forms of commonality across quantiles, leading to more efficient quantile estimation, especially in the data sparse areas. 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 regression estimators. Computational issues and the use of informative priors will also be discussed. Finally, we use the BEL approach to quantile regression as a statistical downscaling method in climate studies, and illustrate by example the merit of our proposed BEL approach.
There will be tea in SEO 300 after the colloquium.
Thursday January 20, 2011 at 3:00 PM in SEO 636