On the rate of convergence of the functional k-nearest neighbor estimates - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles IEEE Transactions on Information Theory Year : 2010

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.
No file

Dates and versions

hal-00911993 , version 1 (01-12-2013)

Identifiers

Cite

Gérard Biau, Frédéric Cérou, Arnaud Guyader. On the rate of convergence of the functional k-nearest neighbor estimates. IEEE Transactions on Information Theory, 2010, IT-56 (4), pp.2034-2040. ⟨10.1109/TIT.2010.2040857⟩. ⟨hal-00911993⟩
228 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More