Regression Discontinuity Designs for Functional Data and Random Objects in Geodesic Spaces
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| author | Kurisu, Daisuke Zhou, Yidong Otsu, Taisuke Müller, Hans-Georg |
| author_facet | Kurisu, Daisuke Zhou, Yidong Otsu, Taisuke Müller, Hans-Georg |
| contents | Regression discontinuity designs have been widely used in observational studies to estimate causal effects of an intervention or treatment at a cutoff point. We propose a generalization of regression discontinuity designs to handle complex non-Euclidean outcomes, such as networks, compositional data, functional data, and other random objects residing in geodesic metric spaces. A key challenge in this setting is the absence of algebraic operations, which makes it difficult to define treatment effects using simple differences. To address this, we define the causal effect at the cutoff as a geodesic between the local Fréchet means of untreated and treated outcomes. This reduces to the classical average treatment effect in the scalar case. Estimation is carried out using local Fréchet regression, a nonparametric method for metric space-valued responses that generalizes local linear regression. We introduce a new bandwidth selection procedure tailored to regression discontinuity designs, which performs competitively even in classical scalar scenarios. The proposed geodesic regression discontinuity design method is supported by theory, including convergence rate guarantees, and is demonstrated in applications where causal inference is of interest in complex outcome spaces. These include changes in daily CO concentration curves following the introduction of the Taipei Metro, and shifts in UK voting patterns measured by vote share compositions after Conservative Party wins. We also develop an extension to fuzzy designs with non-Euclidean outcomes, broadening the scope of causal inference to settings that allow for imperfect compliance with the assignment rule. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18136 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regression Discontinuity Designs for Functional Data and Random Objects in Geodesic Spaces Kurisu, Daisuke Zhou, Yidong Otsu, Taisuke Müller, Hans-Georg Methodology 62D20, 62R20 Regression discontinuity designs have been widely used in observational studies to estimate causal effects of an intervention or treatment at a cutoff point. We propose a generalization of regression discontinuity designs to handle complex non-Euclidean outcomes, such as networks, compositional data, functional data, and other random objects residing in geodesic metric spaces. A key challenge in this setting is the absence of algebraic operations, which makes it difficult to define treatment effects using simple differences. To address this, we define the causal effect at the cutoff as a geodesic between the local Fréchet means of untreated and treated outcomes. This reduces to the classical average treatment effect in the scalar case. Estimation is carried out using local Fréchet regression, a nonparametric method for metric space-valued responses that generalizes local linear regression. We introduce a new bandwidth selection procedure tailored to regression discontinuity designs, which performs competitively even in classical scalar scenarios. The proposed geodesic regression discontinuity design method is supported by theory, including convergence rate guarantees, and is demonstrated in applications where causal inference is of interest in complex outcome spaces. These include changes in daily CO concentration curves following the introduction of the Taipei Metro, and shifts in UK voting patterns measured by vote share compositions after Conservative Party wins. We also develop an extension to fuzzy designs with non-Euclidean outcomes, broadening the scope of causal inference to settings that allow for imperfect compliance with the assignment rule. |
| title | Regression Discontinuity Designs for Functional Data and Random Objects in Geodesic Spaces |
| topic | Methodology 62D20, 62R20 |
| url | https://arxiv.org/abs/2506.18136 |