Gaussian Copula Function-on-Scalar Regression in Reproducing Kernel Hilbert Space

• Author / Creator

  Xie, Haihan

• This thesis proposes a novel Gaussian copula function-on-scalar regression, which is more flexible to characterize the relationship between functional or image response and scalar predictors and is able to relax the linear assumption in traditional function-on-scalar linear regression. Estimation and prediction of the proposed model are investigated: we develop the closed form for the estimator of coefficient functions in a reproducing kernel Hilbert space without the knowledge of marginal transformations; A valid prediction band is constructed via conformal prediction methods with minimal assumptions. Theoretically, we establish the optimal convergence rate on the estimation of coefficient functions and show that our proposed estimator achieves the minimax rate under both fixed and random designs. Simulations and real data analysis are conducted to assess the finite-sample performance.

• Subjects / Keywords

  • Function-on-scalar regression
  • Gaussian copula model
  • Conformal inference
  • Reproducing Kernel Hilbert Space
  • Minimax rate

• Graduation date

  Fall 2021

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-2r8w-p737

• 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.