Robust change-point detection for functional time series based on U-statistics and dependent wild bootstrap

IF 1.2 3区数学 Q2 STATISTICS & PROBABILITY

Statistical Papers Pub Date : 2024-06-05 DOI:10.1007/s00362-024-01577-7

Lea Wegner, Martin Wendler

引用次数: 0

Abstract

The aim of this paper is to develop a change-point test for functional time series that uses the full functional information and is less sensitive to outliers compared to the classical CUSUM test. For this aim, the Wilcoxon two-sample test is generalized to functional data. To obtain the asymptotic distribution of the test statistic, we prove a limit theorem for a process of U-statistics with values in a Hilbert space under weak dependence. Critical values can be obtained by a newly developed version of the dependent wild bootstrap for non-degenerate 2-sample U-statistics.

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基于 U 统计量和依存野生自举法的功能时间序列稳健变化点检测

本文的目的是为函数时间序列开发一种变化点检验，它使用了全部函数信息，与经典的 CUSUM 检验相比，对异常值的敏感性更低。为此，本文将 Wilcoxon 双样本检验推广到函数数据。为了获得检验统计量的渐近分布，我们证明了在弱依赖条件下希尔伯特空间中 U 统计量取值过程的极限定理。临界值可以通过新开发的非退化 2 样本 U 统计量的依赖性自举得到。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistical Papers 数学-统计学与概率论

CiteScore

2.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal Statistical Papers addresses itself to all persons and organizations that have to deal with statistical methods in their own field of work. It attempts to provide a forum for the presentation and critical assessment of statistical methods, in particular for the discussion of their methodological foundations as well as their potential applications. Methods that have broad applications will be preferred. However, special attention is given to those statistical methods which are relevant to the economic and social sciences. In addition to original research papers, readers will find survey articles, short notes, reports on statistical software, problem section, and book reviews.