Distributed Inference for Tail Risks

For measuring tail risk with scarce extreme events, extreme value analysis
is often invoked as the statistical tool to extrapolate to the tail of a distribution.
The presence of large datasets benefits tail risk analysis by providing more
observations for conducting extreme value analysis. However, large datasets can
be stored distributedly preventing the possibility of directly analyzing them. In
this paper, we introduce a comprehensive set of tools for examining the asymptotic
behavior of tail empirical and quantile processes in the setting where data
is distributed across multiple sources, for instance, when data are stored on multiple
machines. Utilizing these tools, one can establish the oracle property for
most distributed estimators in extreme value statistics in a straightforward way.
We provide various examples to demonstrate the practicality and value of our
proposed toolkit.