Application of nonparametric modelling and resampling methods for statistical inference on the structure of multivariate time series

应用非参数建模和重采样方法对多元时间序列结构进行统计推断

• 批准号: 5332912
• 负责人: Professor Dr. Enno Mammen
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2001
• 资助国家: 德国
• 起止时间: 2000-12-31 至 2008-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5332912?language=en
• 关键词: Application; nonparametric; modelling; resampling; methods

Inferential analysis about an underlying process based on a measured time series is an inverse problem. Typically, such analysis results in a number that has to be regarded as a realization of a random variable. Therefore, it is of central importance to establish confidence regions for the true values and enable statistical tests to investigate hypotheses about the underlying dynamics. As a basic tool for the implemention of such procedures resampling methods, i.e. methods that are based on the generation of random artificial data sets, have been used in the recent years. In the mathematical and the physics literature two resampling approaches have been developed: The bootstrap in mathematical statistics, and the method of surrogate data in physics. Up to now there has been not much interaction and exchange of ideas between these to fields of research. The aim of the proposed project is to develop a unified mathematical framework for both approaches. Especially, some shortcomings of the surrogate data approach should be solved.

基于测量的时间序列对潜在过程进行推理分析是一个逆问题。通常，这样的分析产生的数字必须被视为随机变量的实现。因此，建立真实值的置信区域并启用统计测试来调查有关潜在动态的假设至关重要。作为用于实现这种过程的基本工具，近年来已经使用了恢复方法，即基于随机人工数据集的生成的方法。在数学和物理学文献中，已经发展了两种恢复方法：数理统计中的自助法和物理学中的替代数据法。到目前为止，这些研究领域之间没有太多的互动和思想交流。拟议项目的目的是为这两种方法开发一个统一的数学框架。特别是替代数据法的一些不足之处有待解决。