Date of Award

Spring 5-15-2015

Author's School

Graduate School of Arts and Sciences

Author's Department


Degree Name

Doctor of Philosophy (PhD)

Degree Type



We propose new nonparametric Bayesian approaches to quantile regression using

Dirichlet process mixture (DPM) models. All the existing quantile regression methods

based on DPMs require the kernel density to satisfy the quantile constraint, hence the

kernel densities are themselves usually in the form of mixtures. One innovation of our

approaches is that we impose no constraint on the kernel, thus a wide range of densities

can be chosen as the kernels of the DPM model. The quantile constraint is satisfied by a

post-processing of the DPM by a suitable location shift. As a result, our proposed models

use simpler kernels and yet possess great flexibility by mixing over both the location

parameter and the scale parameter. The posterior consistency of our proposed model is

studied carefully. And Markov chain Monte Carlo algorithms are provided for posterior

inference. The performance of our approaches is evaluated using simulated data and real

data. Moreover, we are able to incorporate random effects into our models such that our

approaches can be extended to handle longitudinal data.


English (en)

Chair and Committee

Nan Lin

Committee Members

Siddhartha Chib, Jimin Ding, Todd Kuffner, Mladen Victor Wickerhauser


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