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Nonparametric kernel regression with multiple predictors and multiple shape constraints

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Nonparametric kernel regression with multiple predictors and multiple shape constraints. / Du, Peng; Parmeter, C.F.; Racine, J.S.

In: Statistica Sinica, Vol. 23, No. 3, 01.07.2013, p. 1347-1371.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Harvard

Du, P, Parmeter, CF & Racine, JS 2013, 'Nonparametric kernel regression with multiple predictors and multiple shape constraints', Statistica Sinica, vol. 23, no. 3, pp. 1347-1371. https://doi.org/10.5705/ss.2012.024

APA

Du, P., Parmeter, C. F., & Racine, J. S. (2013). Nonparametric kernel regression with multiple predictors and multiple shape constraints. Statistica Sinica, 23(3), 1347-1371. https://doi.org/10.5705/ss.2012.024

CBE

Du P, Parmeter CF, Racine JS. 2013. Nonparametric kernel regression with multiple predictors and multiple shape constraints. Statistica Sinica. 23(3):1347-1371. https://doi.org/10.5705/ss.2012.024

MLA

Du, Peng, C.F. Parmeter, and J.S. Racine. "Nonparametric kernel regression with multiple predictors and multiple shape constraints". Statistica Sinica. 2013, 23(3). 1347-1371. https://doi.org/10.5705/ss.2012.024

Vancouver

Du P, Parmeter CF, Racine JS. Nonparametric kernel regression with multiple predictors and multiple shape constraints. Statistica Sinica. 2013 Jul 1;23(3):1347-1371. doi: 10.5705/ss.2012.024

Author

Du, Peng ; Parmeter, C.F. ; Racine, J.S. / Nonparametric kernel regression with multiple predictors and multiple shape constraints. In: Statistica Sinica. 2013 ; Vol. 23, No. 3. pp. 1347-1371.

Bibtex

@article{80fc0a4de31c47e790a862daa33c01f0,
title = "Nonparametric kernel regression with multiple predictors and multiple shape constraints",
abstract = "Nonparametric smoothing under shape constraints has recently received much well-deserved attention. Powerful methods have been proposed for imposing a single shape constraint such as monotonicity and concavity on univariate functions. In this paper, we extend the monotone kernel regression method in Hall and Huang (2001) to the multivariate and multi-constraint setting. We impose equality and/or inequality constraints on a nonparametric kernel regression model and its derivatives. A bootstrap procedure is also proposed for testing the validity of the constraints. Consistency of our constrained kernel estimator is provided through an asymptotic analysis of its relationship with the unconstrained estimator. Theoretical underpinnings for the bootstrap procedure are also provided. Illustrative Monte Carlo results are presented and an application is considered.",
author = "Peng Du and C.F. Parmeter and J.S. Racine",
year = "2013",
month = jul,
day = "1",
doi = "10.5705/ss.2012.024",
language = "English",
volume = "23",
pages = "1347--1371",
journal = "Statistica Sinica",
issn = "1017-0405",
publisher = "Academia Sinica Institute of Statistical Science",
number = "3",

}

RIS

TY - JOUR

T1 - Nonparametric kernel regression with multiple predictors and multiple shape constraints

AU - Du, Peng

AU - Parmeter, C.F.

AU - Racine, J.S.

PY - 2013/7/1

Y1 - 2013/7/1

N2 - Nonparametric smoothing under shape constraints has recently received much well-deserved attention. Powerful methods have been proposed for imposing a single shape constraint such as monotonicity and concavity on univariate functions. In this paper, we extend the monotone kernel regression method in Hall and Huang (2001) to the multivariate and multi-constraint setting. We impose equality and/or inequality constraints on a nonparametric kernel regression model and its derivatives. A bootstrap procedure is also proposed for testing the validity of the constraints. Consistency of our constrained kernel estimator is provided through an asymptotic analysis of its relationship with the unconstrained estimator. Theoretical underpinnings for the bootstrap procedure are also provided. Illustrative Monte Carlo results are presented and an application is considered.

AB - Nonparametric smoothing under shape constraints has recently received much well-deserved attention. Powerful methods have been proposed for imposing a single shape constraint such as monotonicity and concavity on univariate functions. In this paper, we extend the monotone kernel regression method in Hall and Huang (2001) to the multivariate and multi-constraint setting. We impose equality and/or inequality constraints on a nonparametric kernel regression model and its derivatives. A bootstrap procedure is also proposed for testing the validity of the constraints. Consistency of our constrained kernel estimator is provided through an asymptotic analysis of its relationship with the unconstrained estimator. Theoretical underpinnings for the bootstrap procedure are also provided. Illustrative Monte Carlo results are presented and an application is considered.

UR - http://www.scopus.com/inward/record.url?scp=84883879522&partnerID=8YFLogxK

U2 - 10.5705/ss.2012.024

DO - 10.5705/ss.2012.024

M3 - Journal article

AN - SCOPUS:84883879522

VL - 23

SP - 1347

EP - 1371

JO - Statistica Sinica

JF - Statistica Sinica

SN - 1017-0405

IS - 3

ER -