Kernel estimation of regression function gradient. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Kroupová, Monika; Horová, Ivana; Koláček, Jan
• Is Part Of: Communications in statistics. Volume 49:Issue 1(2020)
• Page Start: 135
• Page End: 151
• Publication Date: 2020-01-02
• Subjects: Kernel estimation -- regression function gradient -- multivariate regression -- constrained bandwidth matrix -- kernel smoothing -- mean integrated square error; 62G08; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2018.1532518
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: This paper is focused on kernel estimation of the gradient of a multivariate regression function. Despite the importance of this topic, the progress in this area is rather slow. Our aim is to construct a gradient estimator using the idea of local linear estimator for a regression function. The quality of this estimator is expressed in terms of the Mean Integrated Square Error. We focus on a choice of bandwidth matrix. Further, we present some data-driven methods for its choice and develop a new approach. The performance of presented methods is illustrated using a simulation study and real data example.