000234178 001__ 234178
000234178 005__ 20181203024928.0
000234178 0247_ $$2doi$$a10.1214/17-Aap1294
000234178 022__ $$a1050-5164
000234178 02470 $$2ISI$$a000417972700012
000234178 037__ $$aARTICLE
000234178 245__ $$aRobust Bounds In Multivariate Extremes
000234178 260__ $$bInstitute of Mathematical Statistics$$c2017$$aCleveland
000234178 269__ $$a2017
000234178 300__ $$a29
000234178 336__ $$aJournal Articles
000234178 520__ $$aExtreme value theory provides an asymptotically justified framework for estimation of exceedance probabilities in regions where few or no observations are available. For multivariate tail estimation, the strength of extremal dependence is crucial and it is typically modeled by a parametric family of spectral distributions. In this work, we provide asymptotic bounds on exceedance probabilities that are robust against misspecification of the extremal dependence model. They arise from optimizing the statistic of interest over all dependence models within some neighborhood of the reference model. A certain relaxation of these bounds yields surprisingly simple and explicit expressions, which we propose to use in applications. We show the effectiveness of the robust approach compared to classical confidence bounds when the model is misspecified. The results are further applied to quantify the effect of model uncertainty on the Value-at-Risk of a financial portfolio.
000234178 6531_ $$aExtremal dependence
000234178 6531_ $$aPickands' function
000234178 6531_ $$amodel misspecification
000234178 6531_ $$astress test
000234178 6531_ $$arobust bounds
000234178 6531_ $$aconvex optimization
000234178 700__ $$0246548$$g224237$$uEcole Polytech Fed Lausanne, EPFL FSB MATHAA STAT, Stn 8, CH-1015 Lausanne, Switzerland$$aEngelke, Sebastian
000234178 700__ $$aIvanovs, Jevgenijs
000234178 773__ $$j27$$tAnnals Of Applied Probability$$k6$$q3706-3734
000234178 909C0 $$xU10124$$0252136$$pSTAT
000234178 909CO $$pSB$$particle$$ooai:infoscience.tind.io:234178
000234178 917Z8 $$x111184
000234178 937__ $$aEPFL-ARTICLE-234178
000234178 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000234178 980__ $$aARTICLE