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Permanent link (DOI): https://doi.org/10.7939/R3NV99N3G

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Computation in quantile and composite quantile regression models with or without regularization Open Access

Descriptions

Other title
Subject/Keyword
composite quantile regresssion
variable selection
quantile regression
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Gao, Jueyu
Supervisor and department
Gombay, Edit (Mathematical and Statistical Sciences)
Kong, Linglong (Mathematical and Statistical Sciences)
Examining committee member and department
Kong, Linglong (Mathematical and Statistical Sciences)
Niu, Di (Electrical and Computer Engineering)
Gombay, Edit (Mathematical and Statistical Sciences)
Mizera, Ivan (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Statistical Machine Learning
Date accepted
2015-09-29T09:24:19Z
Graduation date
2015-11
Degree
Master of Science
Degree level
Master's
Abstract
Quantile, composite quantile regression with or without regularization have been widely studied and applied in the high-dimensional model estimation and variable selections. Although the theoretical aspect has been well established, the lack of efficient computation methods and publicly available programs or packages hinder the research in this area. Koenker has established and implemented the interior point(IP) method in quantreg for quantile regression with or without regularization. However, it still lacks the ability to handle the composite quantile regression with or without regularization. The same incapability also existed in Coordinate Descent (CD) algorithm that has been implemented in CDLasso. The lack of handful programs for composite quantile regression with or without regularization motivates our research here. In this work, we implement three different algorithms including Majorize and Minimize(MM), Coordinate Descent(CD) and Alternation Direction Method of Multiplier(ADMM) for quantile and composite quantile regression with or without regularization. We conduct the simulation that compares the performance of four algorithms in time efficiency and estimation accuracy. The simulation study shows our program is time efficient when dealing with high dimensional problems. Based on the good performance of our program, we publish the R package cqrReg, which give the user more flexibility and capability when directing various data analyses. In order to optimize the time efficiency, the package cqrReg is coded in C++ and linked back to R by an user-friendly interface.
Language
English
DOI
doi:10.7939/R3NV99N3G
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. 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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