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Main Authors: Zhang, Ping, Wang, Ruoyu, Miao, Wang
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2504.08294
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author Zhang, Ping
Wang, Ruoyu
Miao, Wang
author_facet Zhang, Ping
Wang, Ruoyu
Miao, Wang
contents To answer questions of "causes of effects", the probability of necessity is introduced for assessing whether or not an observed outcome was caused by an earlier treatment. However, the statistical inference for probability of necessity is understudied due to several difficulties, which hinders its application in practice. The evaluation of the probability of necessity involves the joint distribution of potential outcomes, and thus it is in general not point identified and one can at best obtain lower and upper bounds even in randomized experiments, unless certain monotonicity assumptions on potential outcomes are made. Moreover, these bounds are non-smooth functionals of the observed data distribution and standard estimation and inference methods cannot be directly applied. In this paper, we investigate the statistical inference for the probability of necessity in general situations where it may not be point identified. We introduce a mild margin condition to tackle the non-smoothness, under which the bounds become pathwise differentiable. We establish the semiparametric efficiency theory and propose novel asymptotically efficient estimators of the bounds, and further construct confidence intervals for the probability of necessity based on the proposed bounds estimators. The resultant confidence intervals are less conservative than existing methods and can effectively make use of the observed covariates.
format Preprint
id arxiv_https___arxiv_org_abs_2504_08294
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Causal attribution with confidence
Zhang, Ping
Wang, Ruoyu
Miao, Wang
Methodology
To answer questions of "causes of effects", the probability of necessity is introduced for assessing whether or not an observed outcome was caused by an earlier treatment. However, the statistical inference for probability of necessity is understudied due to several difficulties, which hinders its application in practice. The evaluation of the probability of necessity involves the joint distribution of potential outcomes, and thus it is in general not point identified and one can at best obtain lower and upper bounds even in randomized experiments, unless certain monotonicity assumptions on potential outcomes are made. Moreover, these bounds are non-smooth functionals of the observed data distribution and standard estimation and inference methods cannot be directly applied. In this paper, we investigate the statistical inference for the probability of necessity in general situations where it may not be point identified. We introduce a mild margin condition to tackle the non-smoothness, under which the bounds become pathwise differentiable. We establish the semiparametric efficiency theory and propose novel asymptotically efficient estimators of the bounds, and further construct confidence intervals for the probability of necessity based on the proposed bounds estimators. The resultant confidence intervals are less conservative than existing methods and can effectively make use of the observed covariates.
title Causal attribution with confidence
topic Methodology
url https://arxiv.org/abs/2504.08294