均值变点估计的强相合性  

Strong consistence of estimator for the change point in mean

作　　者：史晓平[1] 缪柏其[1] 葛春蕾[2] 

机构地区：[1]中国科学技术大学统计与金融系,安徽合肥230026 [2]合肥工业大学数学系,安徽合肥230009

出　　处：《中国科学技术大学学报》2008年第9期1089-1093,共5页JUSTC

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

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.

关 键 词：均值变点 累积和 负相关 截尾 强相合 

分 类 号：O211.4[理学—概率论与数理统计]