Before revision:  Our tests are built on conditional moment embeddings (CMME)---a novel representation of conditional moment restrictions in a reproducing kernel Hilbert space (RKHS)  . After transforming the conditional moment restrictions into a continuum of unconditional counterparts, the test statistic is defined as the maximum moment restriction  within the unit ball of the RKHS.
After revision:  Our tests are built on conditional moment embeddings (CMME)---a novel representation of conditional moment restrictions in a reproducing kernel Hilbert space (RKHS) . After transforming the conditional moment restrictions into a continuum of unconditional counterparts, the test statistic is defined as the maximum moment restriction (MMR) within the unit ball of the RKHS.