arXiv 30 Apr 2023 · Econometrics · publishedJournal of Political Economy (2026) · 1 citations (OpenAlex)
arXiv:2305.00403 · PDF · DOI · OpenAlex · Extracted main text
Recent years have seen tremendous advances in the theory and application of sequential experiments. While these experiments are not always designed with hypothesis testing in mind, researchers may still be interested in performing tests after the experiment is completed. The purpose of this paper is to aid in the development of optimal tests for sequential experiments by analyzing their asymptotic properties. Our key finding is that the asymptotic power function of any test can be matched by a test in a limit experiment where a Gaussian process is observed for each treatment, and inference is made for the drifts of these processes. This result has important implications, including a powerful sufficiency result: any candidate test only needs to rely on a fixed set of statistics, regardless of the type of sequential experiment. These statistics are the number of times each treatment has been sampled by the end of the experiment, along with final value of the score (for parametric models) or efficient influence function (for non-parametric models) process for each treatment. We then characterize asymptotically optimal tests under various restrictions such as unbiasedness, \alpha-spending constraints etc. Finally, we apply our our results to three key classes of sequential experiments: costly sampling, group sequential trials, and bandit experiments, and show how optimal inference can be conducted in these scenarios.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | K. Adusumilli, “Risk and optimal policies in bandit experiments,” ar… (2021) Risk and optimal policies in bandit experiments | 1.000 | 5 | 4 | 100% |
| 2 | A. W. Van der Vaart, Asymptotic statistics. 1em plus 0.5em minus 0.4… (2000) | 1.000 | 5 | 4 | 100% |
| 3 | K. Hirano and J. R. Porter, “Asymptotic representations for sequenti… (2023) Asymptotic representations for sequential decisions, adaptive experiments, and batched bandits | 0.971 | 12 | 3 | 92% |
| 4 | L. Le Cam, “A Reduction Theorem for Certain Sequential Experiments.… (1979) A Reduction Theorem for Certain Sequential Experiments. II | 0.928 | 5 | 3 | 80% |
| 5 | K. Adusumilli, “Risk and optimal policies in bandit experiments,” ar… (2022) How to sample and when to stop sampling: The generalized wald problem and minimax policies | 0.909 | 8 | 4 | 75% |
| 6 | A. W. Van Der Vaart and J. Wellner, Weak convergence and empirical p… (1996) | 0.843 | 4 | 4 | 75% |
| 7 | G. Wassmer and W. Brannath, Group sequential and confirmatory adapti… (2016) vol | 0.737 | 3 | 2 | 100% |
| 8 | S. Wager and K. Xu, “Diffusion asymptotics for sequential experiment… (2021) Diffusion asymptotics for sequential experiments | 0.644 | 2 | 2 | 100% |
| 9 | T. Lattimore and C. Szepesvári, Bandit algorithms. 1em plus 0.5em mi… (2020) | 0.511 | 2 | 2 | 50% |
| 10 | CBER, FDA draft guidance. 1em plus 0.5em minus 0.4em Center for Biol… (2016) | 0.511 | 2 | 1 | 100% |
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