Semiparametric Inference for Causal Effects on Functional Outcomes

Fuente: arXiv
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Main Authors: Nie, Junzhu, Ling, Chengxiu, Ran, Mengfei
Format: Preprint
Published: 2026
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author Nie, Junzhu
Ling, Chengxiu
Ran, Mengfei
author_facet Nie, Junzhu
Ling, Chengxiu
Ran, Mengfei
contents Difference-in-differences (DiD) is a cornerstone of causal inference, yet extending it to functional outcomes is not a routine scalar generalization; rather, it entails three fundamental challenges in identification, inference, and observation. This paper develops a comprehensive semiparametric inference framework for functional DiD with discretely observed data. First, we define the functional average treatment effect under parallel trends and derive its efficient influence function (EIF), thereby establishing the semiparametric efficiency bound. Second, leveraging Neyman orthogonality and cross-fitting, we construct a debiased estimator that effectively mitigates regularization bias arising from nonparametric reconstruction. Third, we establish weak convergence of the estimator and propose an asymptotically valid uniform confidence band, enabling a rigorous transition from pointwise to curve-level inference. Finally, we demonstrate that reconstruction error under discrete sampling is asymptotically negligible for semiparametric inference, ensuring practical feasibility. Simulations and empirical applications confirm that the proposed method achieves superior coverage and testing power in finite samples, providing a theoretically grounded and computationally tractable foundation for causal evaluation with functional data.
format Preprint
id arxiv_https___arxiv_org_abs_2605_26964
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Semiparametric Inference for Causal Effects on Functional Outcomes
Nie, Junzhu
Ling, Chengxiu
Ran, Mengfei
Methodology
Applications
Difference-in-differences (DiD) is a cornerstone of causal inference, yet extending it to functional outcomes is not a routine scalar generalization; rather, it entails three fundamental challenges in identification, inference, and observation. This paper develops a comprehensive semiparametric inference framework for functional DiD with discretely observed data. First, we define the functional average treatment effect under parallel trends and derive its efficient influence function (EIF), thereby establishing the semiparametric efficiency bound. Second, leveraging Neyman orthogonality and cross-fitting, we construct a debiased estimator that effectively mitigates regularization bias arising from nonparametric reconstruction. Third, we establish weak convergence of the estimator and propose an asymptotically valid uniform confidence band, enabling a rigorous transition from pointwise to curve-level inference. Finally, we demonstrate that reconstruction error under discrete sampling is asymptotically negligible for semiparametric inference, ensuring practical feasibility. Simulations and empirical applications confirm that the proposed method achieves superior coverage and testing power in finite samples, providing a theoretically grounded and computationally tractable foundation for causal evaluation with functional data.
title Semiparametric Inference for Causal Effects on Functional Outcomes
topic Methodology
Applications
url https://arxiv.org/abs/2605.26964