Bandwidth Selection Problem in Nonparametric Functional Regression

Abstract

The focus of this paper is the nonparametric regression where the predictor is a functional random variable, and the response is a scalar. Functional kernel regression belongs to popular nonparametric methods used for this purpose. The two key problems in functional kernel regression are choosing an optimal smoothing parameter and selecting an appropriate semimetric as a distance measure. The former is the focus of this paper – several data-driven methods for optimal bandwidth selection are described and discussed. The performance of these methods is illustrated in a real data application. A conclusion is drawn that local bandwidth selection methods are more appropriate in the functional setting.

Keywords

• Functional data
• nonparametric regression
• kernel methods
• bandwidth selection