Nonparametric Bayesian Quantile Regression via Dirichlet Process Mixture Models

We propose new nonparametric Bayesian approaches to quantile regression usingDirichlet process mixture (DPM) models. All the existing quantile regression methodsbased on DPMs require the kernel density to satisfy the quantile constraint, hence thekernel densities are themselves usually in the form of mixtures. One innovation of ourapproaches is that we impose no constraint on the kernel, thus a wide range of densitiescan be chosen as the kernels of the DPM model. The quantile constraint is satisfied by apost-processing of the DPM by a suitable location shift. As a result, our proposed modelsuse simpler kernels and yet possess great flexibility by mixing over both the locationparameter and the scale parameter. The posterior consistency of our proposed model isstudied carefully. And Markov chain Monte Carlo algorithms are provided for posteriorinference. The performance of our approaches is evaluated using simulated data and realdata. Moreover, we are able to incorporate random effects into our models such that ourapproaches can be extended to handle longitudinal data.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2015

Author dc:creator

• Chang, Chao

Contributors dc:contributor

• Nan Lin
• Siddhartha Chib, Jimin Ding, Todd Kuffner, Mladen Victor Wickerhauser

• Dirichlet Process Mixture
• Nonparametric Bayesian
• Posterior Consistency
• Quantile Regression
• Mathematics

Statement dc:rights

• I have not registered my thesis with the U.S. Copyright Office, and do not intend to.

Language dc:language

English (en)

Identifier

https://openscholarship.wustl.edu/art_sci_etds/458

OAI identifier oai:identifier

oai:openscholarship.wustl.edu:art_sci_etds-1458