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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 m≪n. 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 language | English |
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Pages (from-to) | 244-254 |
Journal | Information Sciences |
Volume | 547 |
Online published | 15 Aug 2020 |
DOIs | |
Publication status | Published - 8 Feb 2021 |
Research Keywords
- Dimension reduction
- Kernel method
- Nonparametric quantile regression
- Random projection
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Dive into the research topics of 'Approximate nonparametric quantile regression in reproducing kernel Hilbert spaces via random projection'. Together they form a unique fingerprint.Projects
- 2 Finished
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GRF: Low-rank tensor as a Dimension Reduction Tool in Complex Data Analysis
LIAN, H. (Principal Investigator / Project Coordinator)
1/01/20 → 28/11/24
Project: Research
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GRF: Divide and Conquer in High-dimensional Statistical Models
LIAN, H. (Principal Investigator / Project Coordinator)
1/10/18 → 24/08/23
Project: Research