Nonparametric Sequential Change-Point Detection by a Vertically Trimmed Box Method

This paper examines a new method for sequential detection of a sudden and unobservable change in a sequence of independent observations with completely unspecified distribution functions. A nonparametric detection rule is proposed which relies on the concept of a moving vertically trimmed box. As su...

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Bibliographic Details
Published in:IEEE transactions on information theory 2010-07, Vol.56 (7), p.3621-3634
Main Authors: Rafajłowicz, Ewaryst, Pawlak, Miroslaw, Steland, Ansgar
Format: Article
Language:English
Subjects:
Additive noise
Average run length
Biomedical signal processing
change in mean
change-point
Control charts
Counting
Data analysis
Data points
Data processing
Delay
Distribution functions
exponential bounds
Information processing
Monitoring
nonparametric inference
Optimization methods
Parameter estimation
Quality control
Signal analysis
Simulation
Tuning
Vanadium
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Summary:This paper examines a new method for sequential detection of a sudden and unobservable change in a sequence of independent observations with completely unspecified distribution functions. A nonparametric detection rule is proposed which relies on the concept of a moving vertically trimmed box. As such, it will be coined as the Vertical Box Control Chart (V-Box Chart). Its implementation requires merely to count the number of data points which fall into the box attached to the last available observation. No a priori knowledge of data distributions is required and proper tuning of the box size provides a quick detection technique. This is supported by establishing statistical properties of the method which explain the role of the tuning parameters used in the V-Box Chart. These theoretical results are verified by simulation studies which indicate that the V-Box Chart may provide quick detection with zero delay for jumps of moderate sizes. Its averaged run length to detection is more favorable than the one for the classical EWMA method. By comparison with the classical Shewhart chart, which was optimized for normal errors, our method provides comparable or better performance.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2010.2048443