Optimal Tests Following Sequential Experiments

Karun Adusumilli

Journal of Political Economy, 2026, vol. 134, issue 9, 2778 - 2823

Abstract: We develop methods for inference following sequential experiments by studying the asymptotic properties of tests. We find that the large-sample power of any test can be matched by a test in a suitable limit experiment involving Gaussian diffusions. This establishes that a fixed set of statistics are asymptotically sufficient for testing; these are the number of times each treatment has been sampled and the final value of the score/efficient influence function process for each treatment. We also derive asymptotically optimal tests under various conditions and apply these findings to three types of sequential experiments: costly sampling, group sequential trials, and bandit experiments.

Date: 2026
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