Detecting a change point using statistical sensitivity analysis based on the influence function

In the field of statistics, when we construct prediction and decision-making models on the basis of a statistical approach, we usually employ previous data to do so. Statistical sensitivity analysis plays an important role in the assessment of these statistical models because it can detect influential observations for the target models, which can enhance their accuracy. However, thus far, it appears that many researchers have developed statistical sensitivity analysis with the assumption that the population parameters for the target data remain flat. Therefore, if the population parameters are not static, a traditional statistical sensitivity analysis cannot exactly evaluate the influence of each observation for target statistical models or parameters. Under these conditions, we must pay attention to not only the influential data point, given as an outlier, but also the change point, which is the point in time when the population parameters of the target data change. In this paper, we propose a sequential statistical approach for detecting a change point by extending the existing statistical sensitivity analysis based on influence functions. Through some numerical simulation studies, we demonstrate the performance of our diagnostic approach.