Nonlinear regression modeling and detecting change points via the relevance vector machine

Abstract

We consider the problem of constructing nonlinear regression models in the case that the structure of data has discontinuities at some unknown points. We propose two-stage procedure in which the change points are detected by relevance vector machine at the first stage, and the smooth curve are effectively estimated along with the technique of regularization method at the second. In order to select tuning parameters in the regularization method, we derive a model selection and evaluation criterion from information-theoretic viewpoints. Simulation results and real data analyses demonstrate that our methodology performs well in various situations.