【摘要】 研究了方差变点的加权累积和估计的一些极限性质.证明了这个估计量的相合性和收敛速度,并由此推导出了变点估计量在局部对立假设下的渐近分布的形式,它是一个有偏移的双边布朗运动.通过渐近分布的数值解可以构造出估计量的渐近置信区间.计算机模拟和实际数据分析表明,这个估计量在应用中有很好的表现.更多还原

【Abstract】 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.更多还原