7 papers
Minimax Boundary Estimation and Estimation with Boundary
Eddie Aamari, Catherine Aaron, Clément Levrard
We derive non-asymptotic minimax bounds for the Hausdorff estimation of -dimensional submanifolds with (possibly) non-empty boundary . The m…
Estimation of surface area
Catherine Aaron, Alejandro Cholaquidis, Ricardo Fraiman
We study the problem of estimating the surface area of the boundary of a sufficiently smooth set when the available information is only a finite…
Robust Fusion Methods for Structured Big Data
Catherine Aaron, Alejandro Cholaquidis, Ricardo Fraiman +1
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 wh…
Robust Fusion Methods for Big Data
Catherine Aaron, Alejandro Cholaquidis, Ricardo Fraiman +1
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 wh…
Detection of low dimensionality and data denoising via set estimation techniques
Catherine Aaron, Alejandro Cholaquidis, Antonio Cuevas
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}^…
On boundary detection
Catherine Aaron, Alejandro Cholaquidis
Given a sample of a random variable supported by a smooth compact manifold , we propose a test to decide whether the boundary of is empty or not with no…
A Generalization of the maximal-spacings in several dimensions and a convexity test
Catherine Aaron, Alejandro Cholaquidis, Ricardo Fraiman
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…