Simultaneous Multiple Change Points Estimation in Generalized Linear Models

In this paper, the problem of multiple change points estimation is considered for generalized linear models, in which both the number of change-points and their locations are unknown. The proposed method is to first partition the data sequence into segments to construct a new design matrix, secondly convert the multiple change points estimation problem into a variable selection problem, and then apply a regularized model selection technique and obtain the regression coefficient estimation. The consistency of the estimator is established regardless if there is a change point in which the number of coefficients can diverge as the sample size goes to infinity. An algorithm is provided to estimate the multiple change points. Simulation studies are conducted for the logistic and log-linear models. A real data application is also presented.