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Nonparametric estimation of a function from noiseless observations at random points


Nonparametric estimation of a function from noiseless observations at random points

Bauer, Benedikt, Devroye, Luc, Kohler, Michael, Krzyżak, Adam and Walk, Harro (2017) Nonparametric estimation of a function from noiseless observations at random points. Journal of Multivariate Analysis . ISSN 0047259X (In Press)

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Official URL: http://dx.doi.org/10.1016/j.jmva.2017.05.010


In this paper we study the problem of estimating a function from n noiseless observations of function values at randomly chosen points. These points are independent copies of a random variable whose density is bounded away from zero on the unit cube and vanishes outside. The function to be estimated is assumed to be (p,C)-smooth, i.e., (roughly speaking) it is p times continuously differentiable. Our main results are that the supremum norm error of a suitably defined spline estimate is bounded in probability by {ln(n)∕n}p∕d for arbitrary p and d and that this rate of convergence is optimal in minimax sense.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Computer Science and Software Engineering
Item Type:Article
Authors:Bauer, Benedikt and Devroye, Luc and Kohler, Michael and Krzyżak, Adam and Walk, Harro
Journal or Publication:Journal of Multivariate Analysis
Date:19 June 2017
  • Natural Sciences and Engineering Research Council of Canada
Digital Object Identifier (DOI):10.1016/j.jmva.2017.05.010
Keywords:Multivariate scattered data approximation; Rate of convergence; Supremum norm error
ID Code:982656
Deposited By: Danielle Dennie
Deposited On:03 Jul 2017 12:44
Last Modified:01 Jun 2018 00:00


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