Kernel estimation of regression function gradient

J 2020

Kernel estimation of regression function gradient

KROUPOVÁ, Monika, Ivanka HOROVÁ and Jan KOLÁČEK

Basic information

Original name

Kernel estimation of regression function gradient

Authors

KROUPOVÁ, Monika (203 Czech Republic, guarantor, belonging to the institution), Ivanka HOROVÁ (203 Czech Republic, belonging to the institution) and Jan KOLÁČEK (203 Czech Republic, belonging to the institution)

Edition

Communications in Statistics - Theory and Methods, Philadelphia, TAYLOR & FRANCIS INC, 2020, 0361-0926

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10103 Statistics and probability

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

Full Text

Impact factor

Impact factor: 0.893

RIV identification code

RIV/00216224:14310/20:00115009

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1080/03610926.2018.1532518

UT WoS

000499984200011

Keywords in English

multivariate kernel regression; constrained bandwidth matrix; kernel smoothing

Abstract

V originále

The present paper is focused on kernel estimation of the gradient of a multivariate regression function. Despite the importance of estimating partial derivatives of multivariate regression functions, the progress is rather slow. Our aim is to construct the gradient estimator using the idea of a local linear estimator for the regression function. The quality of this estimator is expressed in terms of the Mean Integrated Square Error. We focus on a crucial problem in kernel gradient estimation the choice of bandwidth matrix. Further, we present some data-driven methods for its choice and develop a new approach based on Newton's iterative process. The performance of presented methods is illustrated using a simulation study and real data example.

Links

MUNI/A/1418/2019, interní kód MU

Name: Matematické a statistické modelování 4 (Acronym: MaStaMo4)

Investor: Masaryk University, Category A

Files attached

Kroupova_Horova_Kolacek.pdf

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Citovat

KROUPOVÁ, Monika, Ivanka HOROVÁ and Jan KOLÁČEK. Kernel estimation of regression function gradient. Communications in Statistics - Theory and Methods. Philadelphia: TAYLOR & FRANCIS INC, 2020, vol. 49, No 1, p. 135-151. ISSN 0361-0926. Available from: https://dx.doi.org/10.1080/03610926.2018.1532518.

@article{1450636,
   author = {Kroupová, Monika and Horová, Ivanka and Koláček, Jan},
   article_location = {Philadelphia},
   article_number = {1},
   doi = {http://dx.doi.org/10.1080/03610926.2018.1532518},
   keywords = {multivariate kernel regression; constrained bandwidth matrix; kernel smoothing},
   language = {eng},
   issn = {0361-0926},
   journal = {Communications in Statistics - Theory and Methods},
   title = {Kernel estimation of regression function gradient},
   url = {https://www.tandfonline.com/doi/full/10.1080/03610926.2018.1532518},
   volume = {49},
   year = {2020}
}

TY  - JOUR
ID  - 1450636
AU  - Kroupová, Monika - Horová, Ivanka - Koláček, Jan
PY  - 2020
TI  - Kernel estimation of regression function gradient
JF  - Communications in Statistics - Theory and Methods
VL  - 49
IS  - 1
SP  - 135-151
EP  - 135-151
PB  - TAYLOR & FRANCIS INC
SN  - 03610926
KW  - multivariate kernel regression
KW  - constrained bandwidth matrix
KW  - kernel smoothing
UR  - https://www.tandfonline.com/doi/full/10.1080/03610926.2018.1532518
L2  - https://www.tandfonline.com/doi/full/10.1080/03610926.2018.1532518
N2  - The present paper is focused on kernel estimation of the gradient of a multivariate regression function. Despite the importance of estimating partial derivatives of multivariate regression functions, the progress is rather slow. Our aim is to construct the gradient estimator using the idea of a local linear estimator for the regression function. The quality of this estimator is expressed in terms of the Mean Integrated Square Error. We focus on a crucial problem in kernel gradient estimation the choice of bandwidth matrix. Further, we present some data-driven methods for its choice and develop a new approach based on Newton's iterative process. The performance of presented methods is illustrated using a simulation study and real data example.
ER  -

KROUPOVÁ, Monika, Ivanka HOROVÁ and Jan KOLÁČEK. Kernel estimation of regression function gradient. \textit{Communications in Statistics - Theory and Methods}. Philadelphia: TAYLOR \&{} FRANCIS INC, 2020, vol.~49, No~1, p.~135-151. ISSN~0361-0926. Available from: https://dx.doi.org/10.1080/03610926.2018.1532518.

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