We derive minimax testing errors in a distributed framework where the
data is split over multiple machines and their communication to a central machine is limited to b bits. We investigate both the d- and infinite-dimensional
signal detection problem under Gaussian white noise. We also derive distributed testing algorithms reaching the theoretical lower bounds.
Our results show that distributed testing is subject to fundamentally different phenomena that are not observed in distributed estimation. Among our
findings, we show that testing protocols that have access to shared randomness can perform strictly better in some regimes than those that do not. We
also observe that consistent nonparametric distributed testing is always possible, even with as little as 1-bit of communication and the corresponding
test outperforms the best local test using only the information available at
a single local machine. Furthermore, we also derive adaptive nonparametric
distributed testing strategies and the corresponding theoretical lower bound
