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QUANTILE REGRESSION METHODS IN FUNCTIONAL DATA ANALYSIS

  • Author / Creator
    Yu, Dengdeng
  • In this thesis, we study the partial quantile regression methods in functional data analysis. In the first part, we propose a prediction procedure for the functional linear quantile regression model by using partial quantile covariance techniques and develop a simple partial quantile regression (SIMPQR) algorithm to efficiently extract partial quantile regression (PQR) basis for estimating functional coefficients. In the second part, we propose and implement an alternative formulation of partial quantile regression (APQR) for functional linear model by using block relaxation ideas and finite smoothing techniques. Such reformulation leads to insightful results and motivates new theory, demonstrating consistency and establishing convergence rates by applying advanced techniques from empirical process theory. In the third part, we propose and implement the generalization of PQR procedure to multidimensional functional linear model using tensor decomposition techniques. We also establish and demonstrate the corresponding asymptotic properties. In all three parts, extensive simulations and real data are investigated to show the superiority of our proposed methods, while the advantages of our proposed PQR basis are well demonstrated in various settings for functional linear quantile regression model.

  • Subjects / Keywords
  • Graduation date
    2017-11:Fall 2017
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R3MP4W22G
  • 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
    Doctoral
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Statistics
  • Supervisor / co-supervisor and their department(s)
    • Kong, Linglong (Mathematical and Statistical Sciences)
    • Mizera, Ivan (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Hai Jiang (Electrical and Computer Engineering)
    • Lan Wang (Statistics)
    • Rohana Karunamuni (Mathematical and Statistical Sciences)