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pro vyhledávání: '"Aaron, Catherine"'
We derive non-asymptotic minimax bounds for the Hausdorff estimation of $d$-dimensional submanifolds $M \subset \mathbb{R}^D$ with (possibly) non-empty boundary $\partial M$. The model reunites and extends the most prevalent $\mathcal{C}^2$-type set
Externí odkaz:
http://arxiv.org/abs/2108.03135
We study the problem of estimating the surface area of the boundary $\partial S$ of a sufficiently smooth set $S\subset\mathbb{R}^d$ when the available information is only a finite subset $\X\subset S$. We propose two estimators. The first makes use
Externí odkaz:
http://arxiv.org/abs/2007.08484
We address one of the important problems in Big Data, namely how to combine estimators from different subsamples by robust fusion procedures, when we are unable to deal with the whole sample. We propose a general framework based on the classic idea o
Externí odkaz:
http://arxiv.org/abs/1804.01858
We address one of the important problems in Big Data, namely how to combine estimators from different subsamples by robust fusion procedures, when we are unable to deal with the whole sample.
Externí odkaz:
http://arxiv.org/abs/1705.10157
This work is closely related to the theories of set estimation and manifold estimation. Our object of interest is a, possibly lower-dimensional, compact set $S \subset {\mathbb R}^d$. The general aim is to identify (via stochastic procedures) some qu
Externí odkaz:
http://arxiv.org/abs/1702.05193
Given a sample of a random variable supported by a smooth compact manifold $M\subset \mathbb{R}^d$, we propose a test to decide whether the boundary of $M$ is empty or not with no preliminary support estimation. The test statistic is based on the max
Externí odkaz:
http://arxiv.org/abs/1603.08460
The notion of maximal-spacing in several dimensions was introduced and studied by Deheuvels (1983) for data uniformly distributed on the unit cube. Later on, Janson (1987) extended the results to data uniformly distributed on any bounded set, and obt
Externí odkaz:
http://arxiv.org/abs/1411.2482
Autor:
Aaron, Catherine
On s'intéresse dans cette thèse, à la mise en évidence des propriétés de connexité dans les données à analyser. Dans le cas de l'analyse des données ”classique” (i.e. linéaire), comme les surfaces de séparation des classes sont des hy
Externí odkaz:
http://tel.archives-ouvertes.fr/tel-00308495
http://tel.archives-ouvertes.fr/docs/00/30/84/95/PDF/AaronTH.pdf
http://tel.archives-ouvertes.fr/docs/00/30/84/95/PDF/AaronTH.pdf
Akademický článek
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Publikováno v:
In Journal of Multivariate Analysis March 2019 170:149-161