A k-nearest neighbor approach for functional regression
Résumé
Let (X, Y) be a random pair taking values in H × R, where H is an infinite dimensional separable Hilbert space. We establish weak consistency of a nearest neighbor-type estimator of the regression function of Y on X based on independent observations of the pair (X, Y). As a general strategy, we propose to reduce the infinite dimension of H by considering only the first d coefficients of an expansion of X in an orthonormal system of H, and then to perform k-nearest neighbor regression in R^d. Both the dimension and the number of neighbors are automatically selected from the observations using a simple data-dependent splitting device.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)
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