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

Elena Di Bernardino (), Thomas Laloë (), Véronique Maume-Deschamps () and Clémentine Prieur ()
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Elena Di Bernardino: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon
Thomas Laloë: JAD - Laboratoire Jean Alexandre Dieudonné - UNS - Université Nice Sophia Antipolis (1965 - 2019) - CNRS - Centre National de la Recherche Scientifique
Véronique Maume-Deschamps: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon
Clémentine Prieur: MOISE - Modelling, Observations, Identification for Environmental Sciences - Centre Inria de l'Université Grenoble Alpes - Inria - Institut National de Recherche en Informatique et en Automatique - LJK - Laboratoire Jean Kuntzmann - UPMF - Université Pierre Mendès France - Grenoble 2 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - CNRS - Centre National de la Recherche Scientifique - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology

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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.

Keywords: Level sets; Distribution function; Plug-in estimation; Hausdorff distance; Conditional Tail Expectation (search for similar items in EconPapers)
Date: 2013-02-08
New Economics Papers: this item is included in nep-ecm
Note: View the original document on HAL open archive server: https://hal.science/hal-00580624v3
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Citations: View citations in EconPapers (9)

Published in ESAIM: Probability and Statistics, 2013, 17, pp.236-256. ⟨10.1051/ps/2011161⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00580624

DOI: 10.1051/ps/2011161

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