Data-driven estimation of change-points with mean shift

Asymptotically linear negative quadrant dependent (ALNQD) sequence is more general than negatively associated (NA) sequence and p*-mixing sequence. Based on ALNQD errors, the CUSUM estimator of mean change-point is studied with common conditions. We obtain a limiting distribution of CUSUM estimator, which can be used to judge the existence of mean change-point. Meanwhile, some weak and strong convergence rates are established for the CUSUM estimator of change-point. In addition, a data-driven algorithm of multiple change-point detection is given, which performs better than Lasso algorithm. Last, multiple change-point detection simulations and real data analysis illustrate the accuracy of our results.