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: |
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| 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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