An M-estimation-based Criterion for Simultaneous Change Point Analysis and Variable Selection in a Regression Problem

Abstract

In this paper, an M-estimation-based criterion is proposed for carrying out change point analysis and variable selection simultaneously in linear models with a possible change point, which includes the criterion proposed in Wu (2008) as its special case. Under certain mild conditions, this criterion is shown to be strongly consistent in the sense that with probability one, it chooses the smallest true model for large n. Its byproducts include strongly consistent estimates of the regression coefficients regardless if there is a change point. In case that there is a change point, its byproducts also include a strongly consistent estimate of the change point parameter. In addition, an algorithm is given in light of the algorithm in Wu (2008), which has significantly reduced the computation time needed by the proposed criterion for the same precision for a sample of large size. Data examples including a simulation study and a real data example are also provided.