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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2606.01960 |
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| _version_ | 1866916073900605440 |
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| author | Regis, Marta Serra, Paulo |
| author_facet | Regis, Marta Serra, Paulo |
| contents | We consider the problem of detecting a Return to Baseline (RtB) in high-frequency monitoring data preceding and following an intervention, where the aim is to identify the time at which the data-generating distribution realigns with its pre-intervention distribution. We propose a sequential, distribution-free testing procedure that does not rely on specifying a null model and provides anytime-valid error control. The method relies on ideas from universal inference to define a discrepancy measure that is aggregated into a non-negative super-martingale, and is then empirically cal- ibrated to form an e-process. The calibration is performed using the baseline data, and is thus subject-specific. We establish finite-sample bounds for the calibration error (under a flexible non-parametric assumption), discuss the impact of tuning parameters and computational complexity, and illustrate through simulations and a clinical case study that the procedure accurately detects RtB from monitoring data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01960 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Return-to-Baseline Testing via Empirically Calibrated e-processes Regis, Marta Serra, Paulo Methodology Statistics Theory We consider the problem of detecting a Return to Baseline (RtB) in high-frequency monitoring data preceding and following an intervention, where the aim is to identify the time at which the data-generating distribution realigns with its pre-intervention distribution. We propose a sequential, distribution-free testing procedure that does not rely on specifying a null model and provides anytime-valid error control. The method relies on ideas from universal inference to define a discrepancy measure that is aggregated into a non-negative super-martingale, and is then empirically cal- ibrated to form an e-process. The calibration is performed using the baseline data, and is thus subject-specific. We establish finite-sample bounds for the calibration error (under a flexible non-parametric assumption), discuss the impact of tuning parameters and computational complexity, and illustrate through simulations and a clinical case study that the procedure accurately detects RtB from monitoring data. |
| title | Return-to-Baseline Testing via Empirically Calibrated e-processes |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2606.01960 |