Abstract
Let Y(1), …, Y(n) be a sequence whose underlying mean is a step function with an unknown number of the steps and unknown change points. The detection of the change points, namely the positions where the mean changes, is an important problem in such fields as engineering, economics, climatology and bioscience. This problem has attracted a lot of attention in statistics, and a variety of solutions have been proposed and implemented. However, there is scant literature on the theoretical properties of those algorithms. Here, we investigate a recently developed algorithm called the Screening and Ranking Algorithm (SaRa). We characterize the theoretical properties of SaRa and show its superiority over other commonly used algorithms. In particular, we develop a false discovery rate approach to the multiple change-point problem and show a strong sure coverage property for the SaRa.