Optimal nonparametric change point analysis (Q97722)

Assume a sequence of data collected at \(T\) timepoints and at each time \(t\) there are multiple observations generated from a common distribution \(F_t\). This paper considers a problem of detecting timepoints when there is a change in the distribution function without a parametric assumption on the distribution. A Kolmogorov-Smirnov detector procedure based on CUSUM Kolmogorov-Smirnov statistic is proposed, which is shown to be consistent and optimal. Practical issues, such as selection of tuning parameters in the definition of the procedure, are also considered. Simulation studies are also performed to assess the performance of the proposed method and in relation to other competing methods. Potential advantage of the proposed method is also demonstrated through the application to a micro-array dataset.