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
Abstract
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 
Refereed:  Yes 
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 
Funders: 

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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