Statistical inference for multivariate extremes via a geometric approach

• DOI: 10.1093/jrsssb/qkae030
• Publication Date: 2024-03-28T20:21:29Z
• Authors: Jennifer L Wadsworth; Ryan Campbell
• Keywords: Statistical Inference; Representation; Parametric model

Abstract A geometric representation for multivariate extremes, based on the shapes of scaled sample clouds in light-tailed margins and their so-called limit sets, has recently been shown to connect several existing extremal dependence concepts. However, these results are purely probabilistic, approach itself not fully exploited statistical inference. We outline a method parametric estimation set shape, which includes useful non-/semi-parametric estimate as pre-processing step. More fundamentally, our provides new class asymptotically motivated models tails distributions, such can accommodate any combination simultaneous or non-simultaneous extremes through appropriate forms shape. Extrapolation further into tail distribution is possible via simulation from fitted model. study confirms that methodology very competitive with approaches successfully allow small probabilities regions where other methods struggle. apply two environmental datasets, diagnostics demonstrating good fit.