位置参数变点估计的收敛速度

Convergence rate of location parameter change-point estimator

对至多一个位置参数变点的模型,基于反对称核函数,运用累积和(cumulative sum,CUSUM)方法给出了变点的U统计量型估计量,并研究了变点估计量的相合性和收敛速度,同时也给出了局部对立条件下估计量的相合性.最后进行了不同样本容量和参数设置下变点估计的模拟分析,从直方图可以看出:变点位置越靠近中间位置,估计越精确.模拟结果显示所给出的估计量的有效性.

For the location parameter change point model allowing at most one change,an antisymmetric kernel function was constructed and a change point estimator was proposed with the help of the CUSUM method.The consistency and convergence rate of the change point estimator were studied under normal conditions and its consistency was given under the condition of local alternative hypothesis.Finally,simulation was performed under different sample sizes and parameter settings.From the histograms,the closer the change-point location gets to the middle,the more accurate the estimate is.The results show that our methods are effective.