ALGORITHMIC SUBSAMPLING UNDER MULTIWAY CLUSTERING
提出一种针对多向聚类依赖数据的算法子抽样方法，证明了其在大样本下的理论性质，并通过模拟和实际数据展示其在推断准确性和稳健性上的优势。
This paper proposes a novel method of algorithmic subsampling (data sketching) for multiway cluster-dependent data. We establish a new uniform weak law of large numbers and a new central limit theorem for multiway algorithmic subsample means. We show that algorithmic subsampling allows for robustness against potential degeneracy, and even non-Gaussian degeneracy, of the asymptotic distribution under multiway clustering at the cost of efficiency and power loss due to algorithmic subsampling. Simulation studies support this novel result, and demonstrate that inference with algorithmic subsampling entails more accuracy than that without algorithmic subsampling. We derive the consistency and the asymptotic normality for multiway algorithmic subsampling generalized method of moments estimator and for multiway algorithmic subsampling M-estimator. We illustrate with an application to scanner data for the analysis of differentiated products markets.