Communication-efficient estimation for non-randomly distributed and missing data

Traditional distributed methods rely on two fundamental fundamental assumptions: completeness, which assumes that datasets across local machines be fully observed, and randomness, which stipulates that data be randomly distributed across these machines. Violating these assumptions can significantly impair the statistical efficiency of distributed estimators or even render them inconsistent. In this paper, we focus on distributed estimation for data that is non-randomly and non-uniformly distributed, and contains missing values. Depending on whether the local Hessian matrix can be transformed, we propose two Communication-efficient Pilot One-step Update (CPOU) methods. These methods integrate pilot sampling to guarantee estimator consistency, inverse probability weighting (IPW) to reduce bias arising from missing data, and one-step updating to ensure that the efficiency of the proposed estimators is comparable to that of the global estimator. Theoretical analysis and empirical studies demonstrate the good performance of the proposed methods.