Local Linear Functional Regression based on Weighted Distance-Based Regression

We consider the problem of nonparametrically predicting a scalar response variable y from a functional predictor χ. We have n observations (χi, yi) and we assign a weight wi ∝ K (d(χ, χi)/h) to each χi, where d( · , · ) is a semi-metric, K is a kernel function and h is the bandwidth. Then we fit a Weighted (Linear) Distance-Based Regression, where the weights are as above and the distances are given by a possibly different semi-metric. This approach can be extended to nonparametric predictions from other kind of explanatory variables (e.g., data of mixed type) in a natural way.