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Bayesian quantile linear regression

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Title: Bayesian quantile linear regression
Author(s): Feng, Yang
Director of Research: Chen, Yuguo
Doctoral Committee Chair(s): Chen, Yuguo
Doctoral Committee Member(s): He, Xuming; Liang, Feng; Portnoy, Stephen L.
Department / Program: Statistics
Discipline: Statistics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): Bayesian inference Markov chain Monte Carlo (MCMC) Quantile regression Linearly interpolated density (LID)
Abstract: 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.
Issue Date: 2011-05-25
Rights Information: Copyright 2011 Yang Feng
Date Available in IDEALS: 2011-05-25
Date Deposited: 2011-05

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