Distributed iterative hard thresholding for variable selection in Tobit models

While there is a substantial body of research on high-dimensional regression with left-censored responses, few methods address this problem in a distributed manner. Due to data transmission limitations and privacy concerns, centralizing all data is often impractical, necessitating a method for collaborative learning with distributed data. In this paper, we employ the Iterative Hard Thresholding (IHT) method for the Tobit model to address this challenge, allowing one to directly specify the desired sparsity and offering an alternative estimation and variable selection approach. Theoretical analysis shows that our estimator achieves a nearly minimax-optimal convergence rate using only a few rounds of communication. Its practical performance is evaluated under both the pooled and the distributed setting. The former highlights its competitive estimation efficiency and variable selection performance compared to existing approaches, while the latter demonstrates that the decentralized estimator closely matches the performance of its centralized counterpart. When applied to high-dimensional left-censored HIV viral load data, our method also demonstrates comparable performance.