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A Location-Invariant Estimator of Extremal Quantile Treatment Effects for Heavy-Tailed Distributions

arXiv · AI, language, vision and robotics · article · Sep 3, 2026 · UTC

Quantile treatment effects (QTEs) measure the effect of a treatment on the distribution of an outcome, and their estimation at extreme quantile levels is of central interest in applications where the target quantiles lie far beyond the range of the data. For heavy-tailed potential outcomes, existing extremal QTE estimators rely on extrapolation combined with a causal extreme value index (EVI) estimator, but the resulting estimator is not invariant under a common location shift of the potential outcome distributions, even though the population QTE is. We address this issue in two steps. First,

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