Approximate nonparametric quantile regression in reproducing kernel Hilbert spaces via random projection

Fode Zhang, Rui Li*, Heng Lian

*Corresponding author for this work

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

9 Citations (Scopus)

Abstract

Nonparametric quantile regression is a commonly used nonlinear quantile model. One general and popular approach is based on the use of kernels within a reproducing kernel Hilbert space (RKHS) framework, with the smoothing splines estimation as a special case. However, when the sample size n is large, the computational burden is heavy. Motivated by the recent advances in random projection for kernel nonparametric (mean) ridge regression (KRR), we consider an m-dimensional random projection approach for kernel quantile regression (KQR) with mn. We establish a theoretical result showing that the sketched KQR still achieves the minimax convergence rate when m is at least as large as the effective statistical dimension of the problem. Some Monte Carlo studies are carried out for illustration purposes.
Original languageEnglish
Pages (from-to)244-254
JournalInformation Sciences
Volume547
Online published15 Aug 2020
DOIs
Publication statusPublished - 8 Feb 2021

Research Keywords

  • Dimension reduction
  • Kernel method
  • Nonparametric quantile regression
  • Random projection

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