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

Guangren Yang; Xiaohui Liu; Heng Lian

doi:10.1016/j.jco.2021.101568

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 Reviews › RGC 21 - Publication in refereed journal › peer-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 language	English
Article number	101568
Journal	Journal of Complexity
Volume	66
Online published	3 Apr 2021
DOIs	https://doi.org/10.1016/j.jco.2021.101568
Publication status	Published - Oct 2021

Research Keywords

Functional data
Minimax rate
Quantile regression
Reproducing kernel Hilbert space

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title = "Optimal prediction for high-dimensional functional quantile regression in reproducing kernel Hilbert spaces",

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.",

keywords = "Functional data, Minimax rate, Quantile regression, Reproducing kernel Hilbert space",

author = "Guangren Yang and Xiaohui Liu and Heng Lian",

year = "2021",

month = oct,

doi = "10.1016/j.jco.2021.101568",

language = "English",

volume = "66",

journal = "Journal of Complexity",

issn = "0885-064X",

publisher = "Academic Press Inc.",

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TY - JOUR

T1 - Optimal prediction for high-dimensional functional quantile regression in reproducing kernel Hilbert spaces

AU - Yang, Guangren

AU - Liu, Xiaohui

AU - Lian, Heng

PY - 2021/10

Y1 - 2021/10

N2 - 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.

AB - 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.

KW - Functional data

KW - Minimax rate

KW - Quantile regression

KW - Reproducing kernel Hilbert space

UR - http://www.scopus.com/inward/record.url?scp=85103960276&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85103960276&origin=recordpage

U2 - 10.1016/j.jco.2021.101568

DO - 10.1016/j.jco.2021.101568

M3 - RGC 21 - Publication in refereed journal

SN - 0885-064X

VL - 66

JO - Journal of Complexity

JF - Journal of Complexity

M1 - 101568

ER -

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

Abstract

Research Keywords

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GRF: Distributed Estimation with Random Projection in Reproducing Kernel Hilbert Spaces

GRF: Low-rank tensor as a Dimension Reduction Tool in Complex Data Analysis

GRF: Divide and Conquer in High-dimensional Statistical Models

Cite this

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

Abstract

Research Keywords

Access Output

Other Access Options

Permanent Link

Other Files and Links

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Projects

GRF: Distributed Estimation with Random Projection in Reproducing Kernel Hilbert Spaces

GRF: Low-rank tensor as a Dimension Reduction Tool in Complex Data Analysis

GRF: Divide and Conquer in High-dimensional Statistical Models

Cite this