KROUPOVÁ, Monika, Ivanka HOROVÁ a Jan KOLÁČEK. Kernel estimation of regression function gradient. Communications in Statistics - Theory and Methods. Philadelphia: TAYLOR & FRANCIS INC, 2020, roč. 49, č. 1, s. 135-151. ISSN 0361-0926. Dostupné z: https://dx.doi.org/10.1080/03610926.2018.1532518. |
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@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 a Jan KOLÁČEK. Kernel estimation of regression function gradient. \textit{Communications in Statistics - Theory and Methods}. Philadelphia: TAYLOR \&{} FRANCIS INC, 2020, roč.~49, č.~1, s.~135-151. ISSN~0361-0926. Dostupné z: https://dx.doi.org/10.1080/03610926.2018.1532518.
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