Bootstrap Confidence Intervals for MultipleChange Points Based on Two-Stage Procedures

We consider the problem of constructing the confidence intervals for multiple change points under linear regression models. Based on two-stage procedures(Jin et al, 2016), we utilize the idea of the orthogonal greedy algorithm (OGA)in the cutting stage and the sup-Wald-type test targeted at estimating changepoints is applied in the refining stage. Under some mild conditions, the rates of consistency and asymptotic distribution for the multiple change points estimators are established. We propose a bootstrap procedure for confidence intervals, which adapts to the unknown magnitude of changes and ensures asymptotic validity. These results are evidenced by simulation and real data examples.