摘要
在二阶矩存在下,对于独立序列,考虑了均值变点的累积和(cumulative sum,CUSUM)型估计,通过截尾,证明了估计是强相合的,改进了已知的弱相合结果.作为非独立的情况,考虑了在可靠性理论、渗透理论以及多元统计分析中有着广泛应用的负相关序列,采用了另外一种截尾方法,也证明了均值变点估计的强相合性.
In the case that the second moment exited, the cumulative sum （CUSUM） estimator of the change point in mean for a independent sequence was studied. Through truncation, it was proved that the estimator is strongly consistent, which improves the known consistent results. Furthermore, as a nonindependent case, a negative association （NA） sequence was studied, which is widely applied in reliability, percolation theory and multivariate statistical analysis. Through another means of truncation, strong consistence for the change-point estimator was proved.
基金
国家自然科学基金(10471135)
中国科学技术大学研究生创新基金(KD2006063)资助
关键词
均值变点
累积和
负相关
截尾
强相合
change point in mean
cumulative sum
negative association
truncation
strong consistent
