Maxiset in sup-norm for kernel estimators
Karine Bertin, Vincent Rivoirard
Abstract
In the Gaussian white noise model, we study the estimation of an unknown multidimensional function f in the uniform norm by using kernel methods. The performances of procedures are measured by using the maxiset point of view: we determine the set of functions which are well estimated (at a prescribed rate) by each procedure. So, in this paper, we determine the maxisets associated to kernel estimators and to the Lepski procedure for the rate of convergence of the form ( n/n)/(2+d). We characterize the maxisets in terms of Besov and Hölder spaces of regularity β.
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