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：摘要：统计推断问题在其多种形式中一直是长达数十年广泛研究的对象。大部分研究重点集中在刻画其行为随可用样本数量的变化，而对记忆限制对性能影响的研究相对较少。近年来，这一课题在工程和计算机科学文献中引起了广泛关注。在本综述论文中，我们试图回顾在假设检验、参数估计以及分布性质检验/估计等若干典型问题中，记忆约束下统计推断的最新技术进展。我们讨论了这一发展领域的主要成果，并通过识别反复出现的主题，提取了算法构建的一些基本模块，以及用于推导下界的有用技术。