Kernel Regression Estimation for Functional Data

Abstract

This article provides an overview of recent nonparametric and semiparametric advances in kernel regression estimation for functional data. In particular, it considers the various statistical techniques based on kernel smoothing ideas that have recently been developed for functional regression estimation problems. The article first examines nonparametric functional regression modelling before discussing three popular functional regression estimates constructed by means of kernel ideas, namely: the Nadaraya-Watson convolution kernel estimate, the kNN functional estimate, and the local linear functional estimate. Uniform asymptotic results are then presented. The article proceeds by reviewing kernel methods in semiparametric functional regression such as single functional index regression and partial linear functional regression. It also looks at the use of kernels for additive functional regression and concludes by assessing the impact of kernel methods on practical real-data analysis involving functional (curves) datasets.