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

基于测量时间序列的底层过程的推理分析是一个逆问题。通常，这种分析得出的数字必须被视为一个随机变量的实现。因此，建立真实值的置信区域并使统计检验能够调查有关潜在动态的假设是至关重要的。作为实施这些程序的基本工具，重采样方法，即基于随机人工数据集的生成的方法，近年来已被使用。在数学和物理文献中，已经发展了两种重采样方法：数理统计学中的自举法和物理学中的替代数据法。到目前为止，这些研究领域之间还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。特别要解决代理数据方法的一些缺点。

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.