Nonparametric estimation of an additive quantile regression model

Joel L. Horowitz; Sokbae Lee

doi:10.1198/016214505000000583

Nonparametric estimation of an additive quantile regression model

Joel L. Horowitz^*, Sokbae Lee

^*Corresponding author for this work

Economics

Research output: Contribution to journal › Article › peer-review

116 Scopus citations

Abstract

This article is concerned with estimating the additive components of a nonparametric additive quantile regression model. We develop an estimator that is asymptotically normally distributed with a rate of convergence in probability of n ^-r/(2r+1) when the additive components are r-times continuously differentiable for some r ≥ 2. This result holds regardless of the dimension of the covariates, and thus the new estimator has no curse of dimensionality. In addition, the estimator has an oracle property and is easily extended to a generalized additive quantile regression model with a link function. The numerical performance and usefulness of the estimator are illustrated by Monte Carlo experiments and an empirical example.

Original language	English (US)
Pages (from-to)	1238-1249
Number of pages	12
Journal	Journal of the American Statistical Association
Volume	100
Issue number	472
DOIs	https://doi.org/10.1198/016214505000000583
State	Published - Dec 2005

Funding

Joel L. Horowitz is Charles E. and Emma H. Morrison Professor of Market Economics, Department of Economics, Northwestern University, Evanston, IL 60208 (E-mail: [email protected]). Sokbae Lee is Senior Research Economist, Centre for Microdata Methods and Practice, Institute for Fiscal Studies, and Lecturer, Department of Economics, University College London, London, WC1E 6BT, U.K. (E-mail: [email protected]). The authors thank Andrew Chesher, Hidehiko Ichimura, Roger Koenker, an editor, an associate editor, and two anonymous referees for helpful comments and suggestions and for pointing out some important references. One referee kindly pointed out some mistakes in the proofs of an earlier draft and suggested corrections. Special thanks go to Andrew Chesher for providing encouragement to work on this project. A preliminary version of this article was presented at the Cemmap Workshop on Quantile Regression Methods and Applications, April, 2003, London, U.K., and at the 2004 Far Eastern Meeting of the Econometric Society, June 30–July 2, 2004, Seoul, Korea. The research of Horowitz was supported in part by National Science Foundation grants SES-9910925 and SES-0352675, and this work was supported in part by ESRC grant RES-000-22-0704.

Keywords

Additive model
Dimension reduction
Local polynomial estimation
Nonparametric regression
Quantile regression

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1198/016214505000000583

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title = "Nonparametric estimation of an additive quantile regression model",

abstract = "This article is concerned with estimating the additive components of a nonparametric additive quantile regression model. We develop an estimator that is asymptotically normally distributed with a rate of convergence in probability of n -r/(2r+1) when the additive components are r-times continuously differentiable for some r ≥ 2. This result holds regardless of the dimension of the covariates, and thus the new estimator has no curse of dimensionality. In addition, the estimator has an oracle property and is easily extended to a generalized additive quantile regression model with a link function. The numerical performance and usefulness of the estimator are illustrated by Monte Carlo experiments and an empirical example.",

keywords = "Additive model, Dimension reduction, Local polynomial estimation, Nonparametric regression, Quantile regression",

author = "Horowitz, {Joel L.} and Sokbae Lee",

note = "Funding Information: Joel L. Horowitz is Charles E. and Emma H. Morrison Professor of Market Economics, Department of Economics, Northwestern University, Evanston, IL 60208 (E-mail: [email protected]). Sokbae Lee is Senior Research Economist, Centre for Microdata Methods and Practice, Institute for Fiscal Studies, and Lecturer, Department of Economics, University College London, London, WC1E 6BT, U.K. (E-mail: [email protected]). The authors thank Andrew Chesher, Hidehiko Ichimura, Roger Koenker, an editor, an associate editor, and two anonymous referees for helpful comments and suggestions and for pointing out some important references. One referee kindly pointed out some mistakes in the proofs of an earlier draft and suggested corrections. Special thanks go to Andrew Chesher for providing encouragement to work on this project. A preliminary version of this article was presented at the Cemmap Workshop on Quantile Regression Methods and Applications, April, 2003, London, U.K., and at the 2004 Far Eastern Meeting of the Econometric Society, June 30–July 2, 2004, Seoul, Korea. The research of Horowitz was supported in part by National Science Foundation grants SES-9910925 and SES-0352675, and this work was supported in part by ESRC grant RES-000-22-0704.",

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N2 - This article is concerned with estimating the additive components of a nonparametric additive quantile regression model. We develop an estimator that is asymptotically normally distributed with a rate of convergence in probability of n -r/(2r+1) when the additive components are r-times continuously differentiable for some r ≥ 2. This result holds regardless of the dimension of the covariates, and thus the new estimator has no curse of dimensionality. In addition, the estimator has an oracle property and is easily extended to a generalized additive quantile regression model with a link function. The numerical performance and usefulness of the estimator are illustrated by Monte Carlo experiments and an empirical example.

AB - This article is concerned with estimating the additive components of a nonparametric additive quantile regression model. We develop an estimator that is asymptotically normally distributed with a rate of convergence in probability of n -r/(2r+1) when the additive components are r-times continuously differentiable for some r ≥ 2. This result holds regardless of the dimension of the covariates, and thus the new estimator has no curse of dimensionality. In addition, the estimator has an oracle property and is easily extended to a generalized additive quantile regression model with a link function. The numerical performance and usefulness of the estimator are illustrated by Monte Carlo experiments and an empirical example.

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KW - Local polynomial estimation

KW - Nonparametric regression

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Nonparametric estimation of an additive quantile regression model

Abstract

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Keywords

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