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.
翻译：动态系统尽管具有确定性,但往往表现出看似随机的行为。 因此,动态系统通常代表一种概率模型,其中未知参数必须使用统计方法加以估计。 在测量这种参数估计的不确定性时,靴子陷阱是一个简单而有力的技术。 在本文中,我们为动态系统开发靴子陷阱,不仅通过新颖的 \ textit{continy} Edgeworth 扩展动态系统来建立其一致性,而且还通过新颖的 \ textit{continy} Edgeworth 扩展来建立其二阶效率。 这是首次用计算机模拟来研究这种持续的 Edgeworth 扩展。 此外,我们用计算机模拟来验证关于靴子陷阱的理论结果。
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