A Fast Estimation Method for Mean Change Point in Massive Data Sets

When the sample size is N, the computational complexity of the least squares estimate of mean change point is O(N^2), and it's necessary to reduce the computational complexity in the case of huge data. In this paper, a two-stage fast scanning algorithm is proposed for the estimation of mean change point, and it is proved that this method has the same convergence speed and limiting distribution as the least squares estimation of mean change point, and the optimal complexity of the new algorithm is O(N^4/3\cdot b_n^2/3). We have conducted sufficient data experiments in terms of computation time and estimated efficiency, and the results show that the estimated efficiency of the new and old methods is similar, but the computation time of our method is obviously shortened.