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Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory

Elena Di Bernardino 1 Thomas Laloë 2, * Véronique Maume-Deschamps 1 Clémentine Prieur 3
* Corresponding author
3 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : This paper deals with the problem of estimating the level sets of an unknown distribution function $F$. A plug-in approach is followed. That is, given a consistent estimator $F_n$ of $F$, we estimate the level sets of $F$ by the level sets of $F_n$. In our setting no compactness property is a priori required for the level sets to estimate. We state consistency results with respect to the Hausdorff distance and the volume of the symmetric difference. Our results are motivated by applications in multivariate risk theory. In this sense we also present simulated and real examples which illustrate our theoretical results.
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Submitted on : Friday, September 30, 2011 - 2:07:53 PM
Last modification on : Thursday, November 19, 2020 - 1:00:23 PM
Long-term archiving on: : Tuesday, November 13, 2012 - 2:56:13 PM

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Elena Di Bernardino, Thomas Laloë, Véronique Maume-Deschamps, Clémentine Prieur. Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory. ESAIM: Probability and Statistics, EDP Sciences, 2013, 17, pp.236-256. ⟨10.1051/ps/2011161⟩. ⟨hal-00580624v3⟩

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