Bayesian empirical likelihood for quantile regression

Bayesian inference provides a flexible way of combiningg data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful investigations. This thesis considers the Bayesian empirical likelihood approach to quantile regression. Taking the empirical likelihood into a Bayesian framework, we show that the resultant posterior is asymptotically normal; its mean shrinks towards the true parameter values and its variance approaches that of the maximum empirical likelihood estimator. Through empirical likelihood, the proposed method enables us to explore various forms of commonality across quantiles for efficiency gains in the estimation of multiple quantiles. By using an MCMC algorithm in the computation, we avoid the daunting task of directly maximizing empirical likelihoods. The finite sample performance of the proposed method is investigated empirically, where substantial efficiency gains are demonstrated with informative priors on common features across quantile levels.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2012

Author dc:creator

• Yang, Yunwen

Contributors dc:contributor

• He, Xuming
• Chen, Yuguo
• Koenker, Roger W.
• Portnoy, Stephen L.

• Efficiency
• Empirical likelihood
• High quantiles
• Quantile regression
• Prior
• Posterior.

Statement dc:rights

• Copyright 2011 Yunwen Yang

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/29522

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/29522