We consider the task of distributed parameter estimation using sequentially interactive protocols subject to local information constraints such as bandwidth limitations, local differential privacy, and restricted measurements. We provide a general framework enabling us to derive a variety of (tight) minimax lower bounds under different parametric families of distributions, both continuous and discrete, under any $\ell_p$ loss. Our lower bound framework is versatile, and yields "plug-and-play" bounds that are widely applicable to a large range of estimation problems. For the families considered, we further complement our lower bounds with matching upper bounds.

翻译：我们考虑使用按顺序互动协议进行分布参数估计的任务,但受当地信息限制,如带宽限制、地方差异隐私和限制性测量的限制。我们提供了一个总体框架,使我们能够在连续和离散分布的不同参数组下得出各种(紧)小型下限。我们较低的约束框架是多功能的,并产生广泛适用于大量估算问题的“插件与玩耍”界限。对于被考虑的家庭,我们进一步补充了我们较低的界限,与上界相匹配。