Semiparametric approaches for the inference of univariate and multivariate extremes

Abstract

In this paper, we present several semiparametric approaches for the inference of univariate and multivariate extremes to resolve the tasks from the EVA (2023) Conference Data Challenge. We implement generalized additive models to capture the flexible relationship for point and interval estimations of the conditional quantiles. We also adopt \(L^{p}\)-quantile to estimate the marginal quantiles of extreme levels. To predict probabilities of multivariate extreme events, we implement conditional methods by Heffernan and Tawn (Royal J. Stat. Soc.: Ser. B (Statistical Methodology) 66(3), 497–546, 2004) and Keef et al. (J. Multivar. Anal. 115, 396–404, 2013). We further validate predicted models, evaluating their performance scores constructed based on the notion of an equally extreme level of quantiles and cross-validation to select the best estimates to achieve high accuracy. When estimating the excess probability of 50-dimensional data, we cluster variables with high correlation after simple data exploration and combine the results obtained from each cluster. Finally, we also provide post-mortem analysis based on the ground truth.