Nonparametric estimation of a function from noiseless observations at random points

Benedikt Bauer, Luc Devroye, Michael Kohler, Adam Krzyżak and Harro Walk

Journal of Multivariate Analysis, 2017, vol. 160, issue C, 93-104

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.

Keywords: Multivariate scattered data approximation; Rate of convergence; Supremum norm error (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.jmva.2017.05.010

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