Distributed inference for two‐sample U‐statistics in massive data analysis

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.