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The problem of nonparametrically predicting a scalar response variable from a functional
predictor is considered. A sample of pairs (functional predictor and response) is observed.
When predicting the response for a new functional predictor value, a semi-metric is used to compute the distances between the new and the previously observed functional predictors. Then each pair in the original sample is weighted according to a decreasing function of these distances. A Weighted (Linear) Distance-Based Regression is fitted, 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 kinds of explanatory variables (e.g., data of mixed type) in a natural way.
CitacióBoj, E.; Delicado, P.; Fortiana, J. Distance-based local linear regression for functional predictors. "Computational statistics and data analysis", Febrer 2010, vol. 54, núm. 2, p. 429-437.