Abstract

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.

Committee Chair

Nan Lin

Committee Members

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

Comments

Permanent URL: https://doi.org/10.7936/K7TQ5ZPC

Degree

Doctor of Philosophy (PhD)

Author's Department

Mathematics

Author's School

Graduate School of Arts and Sciences

Document Type

Dissertation

Date of Award

Spring 5-15-2015

Language

English (en)

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Mathematics Commons

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