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

  • Author / Creator
    Gao, Jueyu
  • 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.

  • Subjects / Keywords
  • Graduation date
    2015-11
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R3NV99N3G
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Statistical Machine Learning
  • Supervisor / co-supervisor and their department(s)
    • Kong, Linglong (Mathematical and Statistical Sciences)
    • Gombay, Edit (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Mizera, Ivan (Mathematical and Statistical Sciences)
    • Kong, Linglong (Mathematical and Statistical Sciences)
    • Niu, Di (Electrical and Computer Engineering)
    • Gombay, Edit (Mathematical and Statistical Sciences)