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Title:On detecting jumps in time series: Nonparametric setting PDF Logo
Authors:Pawlak, Mirek
Rafajlowicz, Ewaryst
Steland, Ansgar
Issue Date:2003
Series/Report no.:Technical Report // Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen 2003,28
Abstract:Motivated by applications in statistical quality control and signal analysis, we propose a sequential detection procedure which is designed to detect structural changes, in particular jumps, immediately. This is achieved by modifying a median filter by appropriate kernel-based jump preserving weights (shrinking) and a clipping mechanism. We aim at both robustness and immediate detection of jumps. Whereas the median approach ensures robust smooths when there are no jumps, the modification ensure immediate reaction to jumps. For general clipping location estimators we show that the procedure can detect jumps of certain heights with no delay, even when applied to Banach space valued data. For shrinking medians we provide an asymptotic upper bound for the normed delay. The finite sample properties are studied by simulations which show that our proposal outperforms classical procedures in certain respects.
Subjects:Edge Detection
Nonparametric Estimation
Quality Control
Statistical Process Control
Document Type:Working Paper
Appears in Collections:Technical Reports, SFB 475, TU Dortmund

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