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 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.