# 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; Clémentine Prieur

ESAIM: Probability and Statistics (2013)

- Volume: 17, page 236-256
- ISSN: 1292-8100

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topDi Bernardino, Elena, et al. "Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory." ESAIM: Probability and Statistics 17 (2013): 236-256. <http://eudml.org/doc/274392>.

@article{DiBernardino2013,

abstract = {This paper deals with the problem of estimating the level sets L(c) = \{F(x) ≥ c\}, with c ∈ (0,1), of an unknown distribution function F on ℝ+2. A plug-in approach is followed. That is, given a consistent estimator Fn of F, we estimate L(c) by Ln(c) = \{Fn(x) ≥ c\}. In our setting, non-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 particular we propose a new bivariate version of the conditional tail expectation by conditioning the two-dimensional random vector to be in the level set L(c). We also present simulated and real examples which illustrate our theoretical results.},

author = {Di Bernardino, Elena, Laloë, Thomas, Maume-Deschamps, Véronique, Prieur, Clémentine},

journal = {ESAIM: Probability and Statistics},

keywords = {level sets; distribution function; plug-in estimation; Hausdorff distance; conditional tail expectation},

language = {eng},

pages = {236-256},

publisher = {EDP-Sciences},

title = {Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory},

url = {http://eudml.org/doc/274392},

volume = {17},

year = {2013},

}

TY - JOUR

AU - Di Bernardino, Elena

AU - Laloë, Thomas

AU - Maume-Deschamps, Véronique

AU - Prieur, Clémentine

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

JO - ESAIM: Probability and Statistics

PY - 2013

PB - EDP-Sciences

VL - 17

SP - 236

EP - 256

AB - This paper deals with the problem of estimating the level sets L(c) = {F(x) ≥ c}, with c ∈ (0,1), of an unknown distribution function F on ℝ+2. A plug-in approach is followed. That is, given a consistent estimator Fn of F, we estimate L(c) by Ln(c) = {Fn(x) ≥ c}. In our setting, non-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 particular we propose a new bivariate version of the conditional tail expectation by conditioning the two-dimensional random vector to be in the level set L(c). We also present simulated and real examples which illustrate our theoretical results.

LA - eng

KW - level sets; distribution function; plug-in estimation; Hausdorff distance; conditional tail expectation

UR - http://eudml.org/doc/274392

ER -

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