Application of the bootstrap method for change points analysis in generalized linear models

In this paper, we focus on the construction methods of the prediction model, estimation methods of the change point locations, and the confidence intervals for the generalized linear model with piecewise different coefficients. As a standard approach for multiple change point analysis, the application of the hierarchical splitting algorithm is widely used. However, the hierarchical splitting algorithm has a high risk in that the standard error of the change point estimators become large and, therefore, the prediction accuracy of the estimated model decreases. To deal with this problem, we consider the application of a bootstrap method based on the hierarchical splitting algorithm. Through simulation studies, we compare the algorithms in terms of the prediction accuracy of the estimated model, bias and variance of the change point estimators, and the accuracy of the confidence intervals of the change points. From the result, we confirmed the utility of the bootstrap-based methods for change point analysis, especially the increased prediction accuracy of the obtained model, decreased standard error of the change point estimators, and construction of better confidence intervals depending on the situation. We also present the results of a simple example to demonstrate the utility of the method.