Distributed Inference for Tail Empirical and Quantile Processes

The availability of massive datasets allows for conducting extreme value statistics using more observations drawn from the tail of an underlying distribution. When large datasests are distributedly stored and cannot be combined into one oracle sample, a divide-and-conquer algorithm is often invoked to construct a distributed estimator. If the distributed estimator possesses the same asymptotic behavior as the hypothetical oracle estimator based on the oracle sample, then it is regarded as satisfying the oracle property. In this paper, we introduce a set of tools regarding the asymptotic behavior of the tail empirical and quantile processes under the distributed inference setup. Using these tools, one can easily establish the oracle property for most extreme value estimators based on the peak-over-threshold approach. We provide various examples to show the usefulness of the tools.