This paper considers distributed inference for two‐sample U‐statistics under the massive data setting. In order to reduce the computational complexity, this paper proposes distributed two‐sample U‐statistics and blockwise linear two‐sample U‐statistics. The blockwise linear two‐sample U‐statistic, which requires less communication cost, is more computationally efficient especially when the data are stored in different locations. The asymptotic properties of both types of distributed two‐sample U‐statistics are established. In addition, this paper proposes bootstrap algorithms to approximate the distributions of distributed two‐sample U‐statistics and blockwise linear two‐sample U‐statistics for both nondegenerate and degenerate cases. The distributed weighted bootstrap for the distributed two‐sample U‐statistic is new in the literature. The proposed bootstrap procedures are computationally efficient and are suitable for distributed computing platforms with theoretical guarantees. Extensive numerical studies illustrate that the proposed distributed approaches are feasible and effective.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.