The problem of statistical inference in its various forms has been the subject of decades-long extensive research. Most of the effort has been focused on characterizing the behavior as a function of the number of available samples, with far less attention given to the effect of memory limitations on performance. Recently, this latter topic has drawn much interest in the engineering and computer science literature. In this survey paper, we attempt to review the state-of-the-art of statistical inference under memory constraints in several canonical problems, including hypothesis testing, parameter estimation, and distribution property testing/estimation. We discuss the main results in this developing field, and by identifying recurrent themes, we extract some fundamental building blocks for algorithmic construction, as well as useful techniques for lower bound derivations.

翻译：各类统计推断问题数十年来一直是广泛研究的主题。大部分研究集中于刻画性能随可用样本数量的变化规律，而对内存限制如何影响性能的关注则少得多。近期，这一课题在工程与计算机科学文献中引起了广泛兴趣。本综述论文试图回顾若干典型问题（包括假设检验、参数估计及分布性质检验/估计）中内存约束下统计推断的最新进展。我们讨论这一发展领域的主要成果，并通过识别反复出现的主题，提炼出算法构建的基本模块以及下界推导的有效技术。