Bayesian quantile linear regression

Quantile regression, as a supplement to the mean regression, is often used when a comprehensive relationship between the response variable and the explanatory variables is desired. The traditional frequentists’ approach to quantile regression was well developed with asymptotic theories and efficient algorithms. However not much work has been done under the Bayesian framework. The most challenging problem for Bayesian quantile regression is that the likelihood is usually not available unless a certain distribution for the error is assumed. In this dissertation, we propose two Bayesian quantile regression methods: the data generating process based method (DG) and the linearly interpolated density based method (LID). Markov chain Monte Carlo algorithms are developed to implement the proposed methods. We provide the convergence property of the algorithms and numerically verify the theoretical results. We compare the proposed methods with some existing methods through simulation studies, and apply our method to the birth weight data. Unlike most of the existing methods which aim at tackling one quantile at a time, our proposed methods aim at estimating the joint posterior distribution of multiple quantiles and achieving global efficiency for all quantiles of interest and functions of those quantiles. From the simulation results, we found that LID could produce more efficient estimates than some existing methods. In particular, for estimating the difference of quantiles, LID has a big advantage over other existing methods.

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

2011

Author dc:creator

• Feng, Yang

Contributors dc:contributor

• Chen, Yuguo
• He, Xuming
• Liang, Feng
• Portnoy, Stephen L.

• Bayesian inference
• Markov chain Monte Carlo (MCMC)
• Quantile regression
• Linearly interpolated density (LID)

Statement dc:rights

• Copyright 2011 Yang Feng

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/24348

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/24348