Proposal Description

The last decades extreme value inference has developed enormously. First the emphasis was on univariate data, but then also multivariate and functional data have been considered. Statistical theory as well as applications in many fields (e.g., climate research, finance, insurance, longevity, seismology, hydrology, sports records, corrosion engineering) have been studied extensively. The development started for independent and identically distributed data, but once such results were established, not much later corresponding results for time series data were also proved. However the important, general statistical theory for non-identically distributed (non-stationary, heterogeneous) data was lacking until about ten years ago, although several earlier works exist, e.g., for data from limit distributions in extreme value theory and a parametric (linear or loglinear) trend, e.g., Models for exceedances over high thresholds (Davison, Smith; 1990, JRSS B).

The paper Statistics of heteroscedastic extremes (Einmahl, de Haan, Zhou; 2016, JRSS B) develops in a general semiparametric setting the theory for univariate, non-identically distributed data, allowing relatively small deviations from the homogeneous (identically distributed) case. Possibly large heterogeneity has been studied in Trends in extreme value indices (de Haan, Zhou; 2021, JASA) and Extreme value inference for heterogeneous power law data (Einmahl, He, 2023a; Ann. Statist.), but in very different setups. Heterogeneous multivariate regularly varying data have been considered in Statistical inference on a changing extreme value dependence structure (Drees, 2023b; Ann. Statist.).

In the proposed session the 2023a paper will be generalized to an arbitrary extreme value index, very relevant for the many applications where the extreme value index can be zero or negative. Several applications will be presented in detail, in particular to ultimate athletics records. Also, the 2016/2021 papers will be extended to the multivariate case, that is, allowing for heterogeneous tail dependence, also extending the 2023b paper.

The results - theory and applications - presented in the session will be a substantial step forward in the general semiparametric theory of heterogeneous data extremes for univariate and multivariate data. Likely, these results will find many more applications in the near future and also will lead to new theoretical developments, e.g., for functional data.

The participants in this session are leading researchers in extreme value theory and statistics of extremes and publish frequently in the top journals in Statistics, like Ann. Statist., JASA, and JRSS B.