Statistical Learning and Inference For Functional Predictor Models via Reproducing Kernel Hilbert Space

• Author / Creator

  Liu, Meichen

• Functional regression is a cornerstone for understanding complex relationships where predictors or responses (or both) are functions. A particularly powerful framework within this domain is the Reproducing Kernel Hilbert Space (RKHS), which facilitates the handling of infinite-dimensional data through a finite set of parameters.

  This thesis delves into three specific topics within functional regression using RKHS, showcasing innovative methodologies and their applications to real-world data. The first topic explores functional linear expectile regression, a method that offers a nuanced view of conditional response distributions, particularly beneficial for asymmetric distributions or when tail behaviour is of interest. The second topic ventures into functional smoothed score (SS) classification. The study investigates the functional classifier’s generalization ability and convergence property. The last chapter addresses the challenge of estimation and inference for the slope function in logistic regression under case-control designs, which exert influence over rare disease research.

  The three topics contribute to functional regression, offering robust and theoretically sound methodologies for analyzing complex data structures. Through the representation theorem of RKHS, this thesis advances statistical modeling techniques and provides practical tools for tackling real-world problems in diverse scientific domains.

• Subjects / Keywords

  • Functional data analysis
  • reproducing kernel Hilbert space

• Graduation date

  Fall 2024

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/r3-z66z-fk92

• License

  This thesis is made available by the University of Alberta Library 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.