动力系统的Bootstrap
The Bootstrap for Dynamical Systems
摘要：
尽管动力系统具有确定性，但它们往往表现出看似随机的行为。因此，动力系统通常由概率模型表示，其未知参数必须使用统计方法来估计。当测量这种参数估计的不确定性时，自助法作为一种简单但功能强大的技术脱颖而出。在本文中，我们发展了动力系统的自举，并建立了它的一致性，但它的二阶效率性通过一个新的\textit{continuous} Edgeworth展开动力系统。这是第一次研究这样的连续Edgeworth展开。此外，我们使用计算机模拟验证了自举的理论结果。
英文摘要：
Despite their deterministic nature, dynamical systems often exhibit seemingly random behaviour. Consequently, a dynamical system is usually represented by a probabilistic model of which the unknown parameters must be estimated using statistical methods. When measuring the uncertainty of such parameter estimation, the bootstrap stands out as a simple but powerful technique. In this paper, we develop the bootstrap for dynamical systems and establish not only its consistency but also its second-order efficiency via a novel \textit{continuous} Edgeworth expansion for dynamical systems. This is the first time such continuous Edgeworth expansions have been studied. Moreover, we verify the theoretical results about the bootstrap using computer simulations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
