Limit properties of weighted cumulative sum estimator of change-point in variance

Some limit properties of the weighted cumulative sum(WCS) estimator for the change-point in variance was studied. The consistency and convergence rate of the estimator were proved. In addition, the asymptotic distribution of the change-point estimator under local alternative hypothesis, which was a two-side Brownian motion with a drift, was developed. By the numerical solution of asymmetric distribution, an asymptotic confidence interval was constructed. Simulation results and a real data example show that the proposed estimator has a good performance in the application.