Convergence of U-Processes in H "older Spaces with Application to Robust\n Detection of a Changed Segment

2019/08/27 by Alfredas Račkauskas, Račkauskas, Alfredas, Martin Wendler +1 · 2 citations
Computer Science · Decision Sciences · Mathematics · #Advanced Statistical Process Monitoring #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1908.10401

openalex publication_date 2019/08/27 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

To detect a changed segment (so called epidemic changes) in a time series,\nvariants of the CUSUM statistic are frequently used. However, they are\nsensitive to outliers in the data and do not perform well for heavy tailed\ndata, especially when short segments get a high weight in the test statistic.\nWe will present a robust test statistic for epidemic changes based on the\nWilcoxon statistic. To study their asymptotic behavior, we prove functional\nlimit theorems for U-processes in H "older spaces. We also study the finite\nsample behavior via simulations and apply the statistic to a real data example.\n

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• Multiple change-points detection based on U-Statistics under weak dependence
• At the edge of Donsker's Theorem: Asymptotics of multiscale scan statistics

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