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QUANTILE REGRESSION METHODS IN FUNCTIONAL DATA ANALYSIS Open Access

Descriptions

Other title
Subject/Keyword
Tensor
PQR
Functional data analysis
SIMPQR
Quantile Regression
ASIMPQR
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Yu, Dengdeng
Supervisor and department
Mizera, Ivan (Mathematical and Statistical Sciences)
Kong, Linglong (Mathematical and Statistical Sciences)
Examining committee member and department
Hai Jiang (Electrical and Computer Engineering)
Rohana Karunamuni (Mathematical and Statistical Sciences)
Lan Wang (Statistics)
Department
Department of Mathematical and Statistical Sciences
Specialization
Statistics
Date accepted
2017-09-28T15:38:44Z
Graduation date
2017-11:Fall 2017
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
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.
Language
English
DOI
doi:10.7939/R3MP4W22G
Rights
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. 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.
Citation for previous publication
D.Yu, L. Kong, and I. Mizera, “Partial functional linear quantile regression for neuroimaging data analysis,” Neurocomputing, vol.195, pp.74-87, 2016.D.Yu, L. Kong, and I. Mizera, “An Alternative Approach to Functional Linear Partial Quantile Regression,” arXiv preprint arXiv:1709.02069.

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File format: pdf (Portable Document Format)
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Last modified: 2017:11:08 17:33:57-07:00
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File title: Introduction and Overview of the Thesis
File title: QUANTILE REGRESSION METHODS IN FUNCTIONAL DATA ANALYSIS
File author: Dengdeng Yu
Page count: 123
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