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A k-nearest neighbor approach for functional regression

Thomas Laloë 1, *
Abstract : 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.
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Thomas Laloë. A k-nearest neighbor approach for functional regression. Statistics and Probability Letters, Elsevier, 2008, 78 (10), pp.1189-1193. ⟨10.1016/j.spl.2007.11.014⟩. ⟨hal-01292692⟩

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