Resampling methods such as the bootstrap have proven invaluable in the field of machine learning. However, the applicability of traditional bootstrap methods is limited when dealing with large streams of dependent data, such as time series or spatially correlated observations. In this paper, we propose a novel bootstrap method that is designed to account for data dependencies and can be executed online, making it particularly suitable for real-time applications. This method is based on an autoregressive sequence of increasingly dependent resampling weights. We prove the theoretical validity of the proposed bootstrap scheme under general conditions. We demonstrate the effectiveness of our approach through extensive simulations and show that it provides reliable uncertainty quantification even in the presence of complex data dependencies. Our work bridges the gap between classical resampling techniques and the demands of modern data analysis, providing a valuable tool for researchers and practitioners in dynamic, data-rich environments.

这篇文章介绍了一种新颖的 Bootstrap 方法，其针对数据依赖关系进行处理，并可在线执行，特别适用于实时应用。作者证明了该 Bootstrap 方案在一般条件下的理论有效性，并通过大量模拟实验表明它能够在复杂的数据依赖关系存在的情况下提供可靠的不确定性量化。本研究架起了经典重采样技术与现代数据分析需求之间的桥梁，为动态、数据丰富的环境中的研究人员和实践者提供了一个有价值的工具。

在线时间序列自举