Peeking with PEAK: Sequential, Nonparametric Composite Hypothesis Tests for Means of Multiple Data Streams

We propose a novel nonparametric sequential test for composite hypotheses for means of multiple data streams. Our proposed method, \emph{peeking with expectation-based averaged capital} (PEAK), builds upon the testing-as-betting framework and provides a non-asymptotic $\alpha$-level test across any stopping time. PEAK is computationally tractable and efficiently rejects hypotheses that are incorrect across all potential distributions that satisfy our nonparametric assumption, enabling joint composite hypothesis testing on multiple streams of data. We numerically validate our theoretical findings under the best arm identification and threshold identification in the bandit setting, illustrating the computational efficiency of our method against state-of-the-art testing methods.