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Maxiset in sup-norm for kernel estimators

Karine Bertin·Vincent Rivoirard
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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 $(\log n/n)^{\be/(2\be+d)}$. We characterize the maxisets in terms of Besov and Hölder spaces of regularity $β$.

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Karine Bertin, Vincent Rivoirard. 2007-01-16. Maxiset in sup-norm for kernel estimators. https://arxiv.org/abs/math/0701446

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