Estimating the locations of multiple change points in the mean
This article deals with the problem of detecting one or more change points. Suppose that there are \(n\) independent observations \(x_{1},\ldots, x_{n}\) from normal distributions all having the same variance. There are \(R\) shifts in the mean subject to \(0\leq R<R_{u}<n\). The location of each shift is \(\tau_{r},\;r=1,\ldots,R\), with \(0<\tau_1<\ldots<\tau_{R}<n\). Given the data and \(R_{u}\) we want to estimate \(R\) and the location of the changes \(\tau_{r}\). A new algorithm is introduced for identifying locations of change points. These location estimates make it computationally feasible to apply the Schwarz information criterion identifying the number of change points maximizing the criterion. For comparisons the single shift method is used with binary segmentation and the proposed method is shown to be superior in detecting two shifts.
scientific article; zbMATH DE number 1865453