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[D M13] Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory
Revue Internationale avec comité de lecture : Journal ESAIM: Probability and Statistics, vol. 17(-), pp. 236-256, 2013, (doi:DOI: http://dx.doi.org/10.1051/ps/2011161)Mots clés: Level sets; distribution function; plug-in estimation; Hausdorff distance; conditional tail expectation
Résumé:
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 â„+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.
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BibTeX
| @article { | |||
| D M13, | |||
| title | = | "{Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory}", | |
| author | = | "E. Di Bernardino and . Laloë and V. Maume-Deschamps and C. Prieur", | |
| journal | = | "ESAIM: Probability and Statistics", | |
| year | = | 2013, | |
| volume | = | 17, | |
| number | = | -, | |
| pages | = | "236-256", | |
| note | = | "{-}", | |
| doi | = | "DOI: http://dx.doi.org/10.1051/ps/2011161", | |
| } | |||
