Analysis of Functional Data without Dimension Reduction: Tests for Covariance Operators and Changepoint Problems

不降维的函数数据分析：协方差算子和变点问题的测试

• 批准号: 412898780
• 负责人: Dr. Martin Wendler
• 金额: --
• 依托单位: Institut für Mathematische Stochastik (IMST)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2018
• 资助国家: 德国
• 起止时间: 2017-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/412898780?language=en
• 关键词: Analysis; Functional; Data; without; Dimension

Functional data arises in many applications and the main strategy for statistical inference is dimension reduction: The data is projected on a finite-dimensional space with techniques such as functional principal components. After this, it is possible to use statistical test for finite-dimensional data. In contrast, there are recent proposals to base the statistical tests on the full functional information, typically modeld as Hilbert-space-valued time series. These methods have been investigated in the context of sample means and simple changepoints.The aim of this project is to develop fully functional methods in more complicated data situations: We will investigate test for hypothesis not on the functional mean, but on the covariance operator. Furthermore, we plan to develop test for changepoints in data including extreme outliers, which might lead to false negatives and false positive results of standard methods. The last part will deal with segmentation of functional time series or detection of multiple changepoints. To get critical values, we will extend nonparametric methods like bootstrap to these challenging data situations.

功能数据出现在许多应用程序中，统计推断的主要策略是降维：使用功能主成分等技术将数据投影到有限维空间上。在此之后，就可以对有限维数据进行统计检验。相反，最近有人建议将统计检验建立在全功能信息的基础上，通常建模为希尔伯特空间值时间序列。这些方法已经在样本均值和简单变化点的背景下进行了研究。该项目的目的是在更复杂的数据情况下开发全功能方法：我们将研究假设检验，而不是在功能均值上，而是在协方差算子上。此外，我们计划对数据中的变化点进行测试，包括极端异常值，这可能导致标准方法的假阴性和假阳性结果。最后将讨论功能时间序列的分割或多个变化点的检测。为了得到临界值，我们将扩展非参数方法，如bootstrap来处理这些具有挑战性的数据情况。