Differentially Private Distributed Inference Based on U‐Statistics for Massive Data

The rapid advancement of information technology has enabled many organizations to collect large‐scale datasets for research and decision‐making. This expansion of data‐driven practices also increases the risk of disclosing sensitive information, making privacy protection a critical concern. Differential privacy has emerged as a widely used framework to address this challenge, offering rigorous, mathematically grounded privacy guarantees. In this paper, we develop estimation and inference tools for U‐statistics on massive datasets under differential privacy. We propose a differentially private distributed estimator for U‐statistics and introduce a corresponding pseudo‐distributed bootstrap procedure for private inference. We establish the large‐sample properties of these methods under some regularity conditions. We evaluate the finite‐sample performance of the proposed methods through comprehensive simulations and real‐data applications.