Optimal distributed Poisson subsampling for modal regression with massive data

Modern statistical analysis often grapples with the challenge of limited computational resources when handling large datasets. Subsampling, a widely adopted solution, is particularly effective in reducing computational burden while maintaining estimation efficiency. However, subsampling with replacement faces memory constraint issues; if the data volume is so large that subsampling probabilities cannot be loaded into memory all at once, it becomes infeasible to implement. To tackle this problem, in this paper, we propose an optimal Poisson subsampling method in the context of modal regression with massive data. A practical two-step algorithm based on the weighted modal expectation-maximization iteration is proposed, and the consistency and asymptotic normality of the resulting estimator are investigated. Additionally, a communication-efficient distributed modal regression method via optimal Poisson subsampling (CDMROS) is developed, with the asymptotic properties of the resultant estimator established. Numerical experiments on both simulated and real data sets are conducted to demonstrate the superior performance of proposed methods.