Spectral Design of Random-Duration Switchbacks
Abstract
A switchback experiment alternates an entire system between treatment and control over time. It is especially useful when interactions between units can undermine standard unit-level experiments. Switchback experiments are commonly implemented on fixed temporal grids, which impose highly structured restrictions on when treatment can switch. We study a broader class of random-duration switchbacks, in which treatment and control alternate across runs whose durations are drawn from a common distribution. Under finite carryover, we show that the mean squared error of the Horvitz-Thompson estimator has a simple frequency-domain representation governed by how temporal outcome patterns align with design-induced imbalance and contamination patterns. This representation yields a tractable worst-case design criterion that can be computed directly from the duration distribution. Optimizing over even a simple two-rate family produces a run-age-dependent switching rule that reduces the asymptotic worst-case mean squared error by at least 32\% relative to the standard independently randomized fixed-block switchback.
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BibTeX
@misc{hu2026spectral,
title = {{Spectral Design of Random-Duration Switchbacks}},
author = {Yuchen Hu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13698},
eprint = {2609.13698},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13698},
}
RIS
TY - UNPB
TI - Spectral Design of Random-Duration Switchbacks
AU - Yuchen Hu
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.13698
UR - https://arxiv.org/abs/2609.13698
AB - A switchback experiment alternates an entire system between treatment and control over time. It is especially useful when interactions between units can undermine standard unit-level experiments. Switchback experiments are commonly implemented on fixed temporal grids, which impose highly structured restrictions on when treatment can switch. We study a broader class of random-duration switchbacks, in which treatment and control alternate across runs whose durations are drawn from a common distribution. Under finite carryover, we show that the mean squared error of the Horvitz-Thompson estimator has a simple frequency-domain representation governed by how temporal outcome patterns align with design-induced imbalance and contamination patterns. This representation yields a tractable worst-case design criterion that can be computed directly from the duration distribution. Optimizing over even a simple two-rate family produces a run-age-dependent switching rule that reduces the asymptotic worst-case mean squared error by at least 32\% relative to the standard independently randomized fixed-block switchback.
ER -