# Randomization Inference When N Equals One

arXiv: https://arxiv.org/abs/2310.16989 · HTML: https://mlsanity.com/paper/2310.16989/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2023.

## Built on by (most cited first, 5 of 5)

- [EdgeBench: Unveiling Scaling Laws of Learning from Real-World Environments](https://mlsanity.com/paper/2607.05155/) (2026)
- [Unraveling the Interplay between Carryover Effects and Reward Autocorrelations in Switchback Experiments](https://mlsanity.com/paper/2403.17285/) (2024)
- [Designing Time Series Experiments in A/B Testing with Transformer Reinforcement Learning](https://mlsanity.com/paper/2602.01853/) (2026)
- [Generalized Fitted Q-Iteration with Clustered Data](https://mlsanity.com/paper/2510.03912/) (2025)
- [Position: Medical AI Neglects Real Treatment Outcomes](https://mlsanity.com/paper/2608.14598/) (2026)

## Abstract (arXiv)

N-of-1 experiments, where a unit serves as its own control and treatment in different time windows, have been used in certain medical contexts for decades. However, due to effects that accumulate over long time windows and interventions that have complex evolution, a lack of robust inference tools has limited the widespread applicability of such N-of-1 designs. This work combines techniques from experiment design in causal inference and system identification from control theory to provide such an inference framework. We derive a model of the dynamic interference effect that arises in linear time-invariant dynamical systems. We show that a family of causal estimands analogous to those studied in potential outcomes are estimable via a standard estimator derived from the method of moments. We derive formulae for higher moments of this estimator and describe conditions under which N-of-1 designs may provide faster ways to estimate the effects of interventions in dynamical systems. We also provide conditions under which our estimator is asymptotically normal and derive valid confidence intervals for this setting.