{"paper":{"title":"Extremal Behavior of Aggregated Data with an Application to Downscaling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.AP"],"primary_cat":"stat.ME","authors_text":"Marco Oesting, Raphael de Fondeville, Sebastian Engelke","submitted_at":"2017-12-28T10:40:00Z","abstract_excerpt":"The distribution of spatially aggregated data from a stochastic process $X$ may exhibit a different tail behavior than its marginal distributions. For a large class of aggregating functionals $\\ell$ we introduce the $\\ell$-extremal coefficient that quantifies this difference as a function of the extremal spatial dependence in $X$. We also obtain the joint extremal dependence for multiple aggregation functionals applied to the same process. Explicit formulas for the $\\ell$-extremal coefficients and multivariate dependence structures are derived in important special cases. The results provide a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09816","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}