Estimation of Treatment Effects in Extreme and Unobserved Data

TL;DR

This paper introduces a novel framework combining Extreme Value Theory and causal inference to estimate treatment effects in rare, impactful events like extreme climate phenomena, addressing a gap in existing methodologies.

Contribution

It develops a consistent estimator for extreme treatment effects using multivariate regular variation, with rigorous performance analysis and validation on synthetic data.

Findings

Estimator performs well on synthetic data

Framework effectively captures effects in rare events

Provides non-asymptotic performance guarantees

Abstract

Causal effect estimation seeks to determine the impact of an intervention from observational data. However, the existing causal inference literature primarily addresses treatment effects on frequently occurring events. But what if we are interested in estimating the effects of a policy intervention whose benefits, while potentially important, can only be observed and measured in rare yet impactful events, such as extreme climate events? The standard causal inference methodology is not designed for this type of inference since the events of interest may be scarce in the observed data and some degree of extrapolation is necessary. Extreme Value Theory (EVT) provides methodologies for analyzing statistical phenomena in such extreme regimes. We introduce a novel framework for assessing treatment effects in extreme data to capture the causal effect at the occurrence of rare events of interest. In particular, we employ the theory of multivariate regular variation to model extremities. We develop a consistent estimator for extreme treatment effects and present a rigorous non-asymptotic analysis of its performance. We illustrate the performance of our estimator using both synthetic and semi-synthetic data.