Combining independent <i>p</i>-values in replicability analysis: a comparative study

Given a family of null hypotheses $H_{1},\ldots,H_{s}$, we are interested in the hypothesis $H_{s}^{\gamma}$ that at most $\gamma-1$ these false. Assuming corresponding $p$-values independent, investigating combined valid for testing $H_{s}^{\gamma}$. In various settings which is false, determine $p$-value works well setting. Via simulations, find Stouffer method if uniformly distributed and signal strength low, Fisher better conservative, i.e. stochastically larger than uniform distribution. The minimum evidence rejection focused on only few non-null $p$-values, especially conservative. Methods incorporate combination $e$-values work $H_{1},\ldots,H_{s}$ simple.