Distributed Inference for Tail Risk

TL;DR

This paper develops tools for analyzing tail risk using distributed data, enabling extreme value analysis across multiple data sources while addressing challenges when the number of sources grows large.

Contribution

It introduces a comprehensive toolkit for tail risk analysis in distributed datasets, including theoretical results for estimators when data sources increase.

Findings

Established oracle properties for distributed estimators

Provided methods for asymptotic analysis in distributed tail risk estimation

Demonstrated practical applications through examples

Abstract

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. The main theoretical challenge arises when the number of machines diverges to infinity. The number of machines resembles the role of dimensionality in high dimensional statistics. We provide various examples to demonstrate the practicality and value of our proposed toolkit.