Sequential Change-Point Problems
In this chapter, we consider the problem of sequential change-point detection. Some well-known sequential methods have already been discussed in Chapter 2: the CUSUM test, the GRSh method, Shewhart’s chart and the exponential smoothing method. All these methods are parametric, i.e. they use a priori information on distributions of a random sequence and/or a change-point. However, it turned out that a nonparametric version can be proposed for anyone of them. Our main goal in this chapter is to compare these nonparametric versions. Our approach to a comparative analysis is based upon the fact that, for most of the sequential change-point detection methods, a “large” parameter N can be proposed, a quantity which when tends to infinity, the probability of “false alarm” tends to zero under relatively broad assumptions, and the “delay time” normalized on N tends to a certain determined limit that can be computed for any method of detection. Besides, there exists an apriori low boundary for this limit and different methods of change-point detection can be compared on the basis of their attainment of, or their proximity to, this boundary, i.e. by the degree of realization of their potential properties.
KeywordsFalse Alarm Exponential Family Exponential Smoothing Dependent Random Variable Asymptotic Optimality
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