Abstract: This short note proposes a stable combination test as a natural extension of the Cauchy combination test. Similarly to the latter, the proposed test is simple to compute, enjoys good size, and has asymptotically optimal power even when the individual tests are not independent. Our simulations demonstrate that the proposed stable combination test may improve the Cauchy combination test if its parameters are chosen carefully.

Key words and phrases: Additive combination test, multiple hypothesis testing, stable distribution.