Kernel estimation of regression function gradient

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.

Keywords:

• Kernel estimation
• regression function gradient
• multivariate regression
• constrained bandwidth matrix
• kernel smoothing
• mean integrated square error

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G08

Additional information

Funding

This research was supported by Masaryk University, project MUNI/A/1204/2017.