Estimation of general semi-parametric quantile regression

Yan Fan; Lixing ZHU

doi:10.1016/j.jspi.2012.11.005

Estimation of general semi-parametric quantile regression

Yan Fan, Lixing ZHU^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

17 Citations (Scopus)

Abstract

Quantile regression introduced by Koenker and Bassett (1978) produces a comprehensive picture of a response variable on predictors. In this paper, we propose a general semi-parametric model of which part of predictors are presented with a single-index, to model the relationship of conditional quantiles of the response on predictors. Special cases are single-index models, partially linear single-index models and varying coefficient single-index models. We propose the qOPG, a quantile regression version of outer-product gradient estimation method (OPG, Xia et al., 2002) to estimate the single-index. Large-sample properties, simulation results and a real-data analysis are provided to examine the performance of the qOPG.

Original language	English
Pages (from-to)	896-910
Number of pages	15
Journal	Journal of Statistical Planning and Inference
Volume	143
Issue number	5
DOIs	https://doi.org/10.1016/j.jspi.2012.11.005
Publication status	Published - May 2013

User-Defined Keywords

Eigenvector
Outer-product gradient estimation (OPG)
QOPG
Quantile regression
Single-index model

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10.1016/j.jspi.2012.11.005

Cite this

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title = "Estimation of general semi-parametric quantile regression",

abstract = "Quantile regression introduced by Koenker and Bassett (1978) produces a comprehensive picture of a response variable on predictors. In this paper, we propose a general semi-parametric model of which part of predictors are presented with a single-index, to model the relationship of conditional quantiles of the response on predictors. Special cases are single-index models, partially linear single-index models and varying coefficient single-index models. We propose the qOPG, a quantile regression version of outer-product gradient estimation method (OPG, Xia et al., 2002) to estimate the single-index. Large-sample properties, simulation results and a real-data analysis are provided to examine the performance of the qOPG.",

keywords = "Eigenvector, Outer-product gradient estimation (OPG), QOPG, Quantile regression, Single-index model",

author = "Yan Fan and Lixing ZHU",

note = "Funding Information: The research described here was supported by a Grant from the University Grants Council of Hong Kong, Hong Kong. The authors thank the editor, the associate editor and a referee for their constructive comments and suggestions which led to a significant improvement on the early paper, particularly an improvement on the theoretical results.",

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AU - Fan, Yan

AU - ZHU, Lixing

N1 - Funding Information: The research described here was supported by a Grant from the University Grants Council of Hong Kong, Hong Kong. The authors thank the editor, the associate editor and a referee for their constructive comments and suggestions which led to a significant improvement on the early paper, particularly an improvement on the theoretical results.

PY - 2013/5

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N2 - Quantile regression introduced by Koenker and Bassett (1978) produces a comprehensive picture of a response variable on predictors. In this paper, we propose a general semi-parametric model of which part of predictors are presented with a single-index, to model the relationship of conditional quantiles of the response on predictors. Special cases are single-index models, partially linear single-index models and varying coefficient single-index models. We propose the qOPG, a quantile regression version of outer-product gradient estimation method (OPG, Xia et al., 2002) to estimate the single-index. Large-sample properties, simulation results and a real-data analysis are provided to examine the performance of the qOPG.

AB - Quantile regression introduced by Koenker and Bassett (1978) produces a comprehensive picture of a response variable on predictors. In this paper, we propose a general semi-parametric model of which part of predictors are presented with a single-index, to model the relationship of conditional quantiles of the response on predictors. Special cases are single-index models, partially linear single-index models and varying coefficient single-index models. We propose the qOPG, a quantile regression version of outer-product gradient estimation method (OPG, Xia et al., 2002) to estimate the single-index. Large-sample properties, simulation results and a real-data analysis are provided to examine the performance of the qOPG.

KW - Eigenvector

KW - Outer-product gradient estimation (OPG)

KW - QOPG

KW - Quantile regression

KW - Single-index model

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U2 - 10.1016/j.jspi.2012.11.005

DO - 10.1016/j.jspi.2012.11.005

M3 - Journal article

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SN - 0378-3758

VL - 143

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EP - 910

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - 5

ER -

Estimation of general semi-parametric quantile regression

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