Distributed estimation is increasingly important due to the explosion of data, enabling accurate estimates by combining data from multiple sources while improving privacy and security by allowing data to stay in its original location. It is essential for managing large-scale data in fields such as finance, healthcare, and environmental monitoring, and plays a critical role in data-driven solutions for a wide range of applications.

In this talk, we focus on distributed minimax estimation and distributed adaptive estimation of Gaussian means and nonparametric regression functions under communication constraints. We establish the minimax rates of convergence for distributed estimation, quantify the exact communication cost for adaptation, and construct optimally adaptive procedures for distributed estimation. Our results highlight significant differences between statistical estimation in the distributed setting and the conventional centralized setting.