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http://bura.brunel.ac.uk/handle/2438/27556
Title: | The Bootstrap for Dynamical Systems |
Authors: | Fernando, K Zou, N |
Keywords: | math.DS;math.DS;math.ST;stat.TH;62F40, 37A50, 62M05 |
Issue Date: | 19-Aug-2021 |
Publisher: | Cornell University |
Citation: | Fernando, K. and Zou, N. (2021) 'The Bootstrap for Dynamical Systems', arXiv:2108.08461 [math.DS], pp. 1 - 51. doi: 10.48550/arXiv.2108.08461. |
Abstract: | 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. |
Description: | The file archived on this institutional repository is a preprint available on arXiv at https://arxiv.org/abs/2108.08461 under a Creative Commons (CC BY) Attribution License. It has not been certified by peer review. |
URI: | https://bura.brunel.ac.uk/handle/2438/27556 |
ISSN: | 2331-8422 |
Other Identifiers: | ORCID iD: Kasun Fernando https://orcid.org/0000-0003-1489-9566 https://arxiv.org/abs/2108.08461v1 |
Appears in Collections: | Dept of Mathematics Research Papers |
Files in This Item:
File | Description | Size | Format | |
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Preprint.pdf | Copyright © 2021 The Author(s). This work is licensed under a Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/). | 1.29 MB | Adobe PDF | View/Open |
This item is licensed under a Creative Commons License