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Permanent link (DOI): https://doi.org/10.7939/R3KX1T

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Hierarchical Quantile Regression Open Access

Descriptions

Other title
Subject/Keyword
quantile regression
Markov Chain Monte Carlo
asymmetric Laplace distribution
data cloning
Bayesian statistics
hierarchical models
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Hassan, Imran
Supervisor and department
Lele, Subhash (Mathematical and Statistical Sciences)
Examining committee member and department
Prasad, NGN (Mathematical and Statistical Sciences)
Cribben, Ivor (School of Business)
Lele, Subhash (Mathematical and Statistical Sciences)
Kong, Linglong (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Biostatistics
Date accepted
2014-08-26T09:23:58Z
Graduation date
2014-11
Degree
Master of Science
Degree level
Master's
Abstract
Quantile regression supplements the ordinary least squares regression and provides a complete view of a relationship between a response variable and a set of covariates. The quantile regression model does not assume any particular error distribution. It is estimated by minimizing an asymmetric absolute error loss function. Bayesian inference of quantile regression is based on the likelihood function formed by independent asymmetric Laplace densities. The asymmetric Laplace distribution is a natural choice for the error distribution of the quantile regression model. However, the model based on the asymmetric Laplace distribution solely focuses on estimation and does not describe the underlying true model. Moreover, it assumes different models for estimating parameters for different quantile levels. In this project, we introduce a hierarchical quantile regression model that removes ambiguities of the quantile regression model based on the asymmetric Laplace distribution. The proposed hierarchical model treats the intercept and the slope of the linear quantile regression model as random effects. The model is estimated by the data cloning method which works in the Bayesian framework exploiting the computational advantage of the Markov Chain Monte Carlo (MCMC) algorithm, but gives the maximum likelihood estimates with standard errors. A simulation study with 50 repetitions has been performed to assess the parameter estimates. We have compared our results to the regular quantile regression estimates for different quantile levels. Our proposed hierarchical model gives a greater insight into the overall quantile regression picture. The model is easily extendable to accommodate more complex situations and provides room for further research.
Language
English
DOI
doi:10.7939/R3KX1T
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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File title: Introduction
File title: Hierarchical Quantile Regression
File author: Imran Hassan
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