Optimal prediction for high-dimensional functional quantile regression in reproducing kernel Hilbert spaces

Guangren Yang, Xiaohui Liu, Heng Lian*

*Corresponding author for this work

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

5 Citations (Scopus)

Abstract

Regression problems with multiple functional predictors have been studied previously. In this paper, we investigate functional quantile linear regression with multiple functional predictors within the framework of reproducing kernel Hilbert spaces. The estimation procedure is based on an ℓ1-mixed-norm penalty. The learning rate of the estimator in prediction loss is established and a lower bound on the learning rate is also presented that matches the upper bound up to a logarithmic term.
Original languageEnglish
Article number101568
JournalJournal of Complexity
Volume66
Online published3 Apr 2021
DOIs
Publication statusPublished - Oct 2021

Research Keywords

  • Functional data
  • Minimax rate
  • Quantile regression
  • Reproducing kernel Hilbert space

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