On the rate of convergence of the functional k-nearest neighbor estimates

Abstract : Let F be a separable Banach space, and let (X, Y) be a random pair taking values in F x R. Motivated by a broad range of potential applications, we investigate rates of convergence of the k-nearest neighbor estimate r_n(x) of the regression function r(x) = E[Y|X = x], based on n independent copies of the pair (X, Y). Using compact embedding theory, we present explicit and general finite sample bounds on the expected squared difference E[(r_n(X) - r(X)]^2], and particularize our results to classical function spaces such as Sobolev spaces, Besov spaces, and reproducing kernel Hilbert spaces.
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IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2010, IT-56 (4), pp.2034-2040. <10.1109/TIT.2010.2040857>
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Contributeur : Francois Le Gland <>
Soumis le : dimanche 1 décembre 2013 - 13:07:12
Dernière modification le : lundi 29 mai 2017 - 14:24:44

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Gérard Biau, Frédéric Cérou, Arnaud Guyader. On the rate of convergence of the functional k-nearest neighbor estimates. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2010, IT-56 (4), pp.2034-2040. <10.1109/TIT.2010.2040857>. <hal-00911993>

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