Using the $k-$nearest neighbor restricted Delaunay complex to estimate the density support and its topological properties - Laboratoire de Mathematiques Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2012

Using the $k-$nearest neighbor restricted Delaunay complex to estimate the density support and its topological properties

Catherine Aaron
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Résumé

We consider random samples in $\mathbb{R}^d$ drawn from an unknown density. This paper is devoted to study the properties of the Delaunay complex restricted to nearest neighbors to estimate the density support and its geometrical properties. We exhibit suitable value for the number of neighbors to be chosen. This value depends on the dimension $d$, the unknown support $S$, the unknown density $f$ and the size of the sample. Since $f$ is continuous and the boundary of $S$ is smooth the value only depends on $d$ and the size of the sample. The convergence of the underlying estimator for the support is proved and a lower bound for the convergence speed is given. A procedure to estimate the topological properties of the support is presented.
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Dates et versions

hal-00672705 , version 1 (21-02-2012)
hal-00672705 , version 2 (03-12-2012)

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  • HAL Id : hal-00672705 , version 1

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Catherine Aaron. Using the $k-$nearest neighbor restricted Delaunay complex to estimate the density support and its topological properties. 2012. ⟨hal-00672705v1⟩
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