Bayesian quantile linear regression

Bayesian inference;Markov chain Monte Carlo (MCMC);Quantile regression;Linearly\rinterpolated density (LID)

Feng, Yang

关键词: Bayesian inference;    Markov chain Monte Carlo (MCMC);    Quantile regression;    Linearly\rinterpolated density (LID);   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/24348/Feng_Yang.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Quantile regression, as a supplement to the mean regression, is often used when a comprehensiverelationship between the response variable and the explanatory variables is desired. The traditionalfrequentists’ approach to quantile regression was well developed with asymptotic theories and efficientalgorithms. However not much work has been done under the Bayesian framework. The mostchallenging problem for Bayesian quantile regression is that the likelihood is usually not availableunless a certain distribution for the error is assumed. In this dissertation, we propose two Bayesianquantile regression methods: the data generating process based method (DG) and the linearly interpolateddensity based method (LID). Markov chain Monte Carlo algorithms are developed toimplement the proposed methods. We provide the convergence property of the algorithms andnumerically verify the theoretical results. We compare the proposed methods with some existingmethods 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 proposedmethods aim at estimating the joint posterior distribution of multiple quantiles and achieving globalefficiency 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.