Date of Award
Spring 5-15-2015
Degree Name
Doctor of Philosophy (PhD)
Degree Type
Dissertation
Abstract
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.
Language
English (en)
Chair and Committee
Nan Lin
Committee Members
Siddhartha Chib, Jimin Ding, Todd Kuffner, Mladen Victor Wickerhauser
Recommended Citation
Chang, Chao, "Nonparametric Bayesian Quantile Regression via Dirichlet Process Mixture Models" (2015). Arts & Sciences Electronic Theses and Dissertations. 458.
https://openscholarship.wustl.edu/art_sci_etds/458
Comments
Permanent URL: https://doi.org/10.7936/K7TQ5ZPC