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Statistical estimation of a multifractal function

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In nonparametric statistics, the accuracy for recovering a density from a sample or a signal corrupted by noise is governed by the smoothness of the target function. This smoothness is usually measured in some global norm like Sobolev or Holder. In this talk, we consider signals with local smoothness that change abruptly from one point to another and that exhibit a so-called multifractal behaviour. We will describe the problem of nonparametric estimation in this setting, relying on the work of Jaffard on the Frish-Parisi conjecture together with the modern formulation of wavelet estimation over atomic spaces by Kerkyacharian and Picard. We will show how the multifractal setting allows to revisit some classical nonparametric estimation results and somehow sheds new light on some specific examples.

This talk is part of the Statistics series.

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