Variable selection in nonparametric regression with functional covariates

We consider a nonparametric regression model with multiple functional covariates, allowing for additional covariates of other types (categorical, continuous). The estimation method is based on an extension of the Nadaraya-Watson estimator, where a kernel function is applied to a linear combination of distance measures, each computed on individual covariates. We are interested in distinguishing between relevant covariates and noise variables. It can be shown that a data-driven least squares cross-validation method can asymptotically remove irrelevant noise variables. Based on this understanding, a thresholded version of the extended Nadaraya-Watson estimator is proposed to perform variable selection.